user8157: In respect to Dependent Origination, the Pali suttas state: 

Vedanā, saññā, cetanā, phasso, manasikāro - idaṃ vuccatāvuso nāmaṃ. Cattāri ca mahābhūtāni catunnañca mahābhūtānaṃ upādāya rūpaṃ. Idaṃ
  vuccatāvuso rūpaṃ. Iti idañca nāmaṃ idañca rūpaṃ - idaṃ vuccatāvuso
  nāmarūpaṃ.
Feeling, perception, volition, contact and attention — these are called mentality. The four great elements and the material form
  derived from the four great elements — these are called materiality.

Alternate translation:

Feeling, perception, intention, contact & attention: This is called name. The four great elements and the form dependent on the four great
  elements: This is called form. This name & this form are called
  name-&-form.

Why do we think 'attention' ('manasikara') is included within 'nama-rupa'? 

Note: I personally do not have a definite answer to this question, apart from personal speculation therefore I have asked the question for people to think about & answer. 

user8157: Very good & helpful answers, including @Saptha Visuddhi's reference to ayonisomanasikāra: 

They are all activity of nāma-rūpa happening only in the present. From this ‘sampassa’ (san+passa) comes Ayonisomanasikāra.

I was giving attention to this in meditation this morning and I decided upon this similar answer: 

Dependent origination arises from ignorance &, of particularly relevance is, the absence of mindfulness & wisdom at sense contact. About this, MN 38 states: 

On seeing a form with the eye, he lusts after it if it is pleasing; he dislikes it if it is unpleasing. He abides with mindfulness of the
  body unestablished, with a limited mind and he does not understand as
  it actually is the deliverance of mind and deliverance by wisdom
  wherein those evil unwholesome states cease without remainder.

In respect to this lack of mindfulness & wisdom, AN 10.61 states:

Lack of mindfulness and clear comprehension, too, has its nutriment; it is not without a nutriment. And what is the nutriment of the lack
  of mindfulness and clear comprehension? 'Unwise attention,' should be
  the answer.
When unwise attention (ayoni­so­ma­nasikāro) prevails, it will make prevail lack of
  mindfulness and clear comprehension.
AN 10.61

In summary, I think attention is included within nama-rupa because ignorance conditions/prepares nama-rupa for unwise/ignorant attention, which in turn will make sense contact unwise/ignorant. 

user-1: 
Why do we think 'attention' ('manasikara') is included within 'nama-rupa'?

Attention is a mental factor (cetasika) that arises based on several other factors, one of those being intention (cetana). It performs one of several cognitive functions that allows for consciousness of an object to arise. This can be experienced through the practice of insight meditation. As this is purely a mental function it is included in Nama-rupa, i.e. the Nama-aspect.
In walking meditation the meditator can experience the four great elements as actual processes (ultimate realities), e.g. the feeling of lightness that occurs in the lifting-phase of the foot. That right there is the experience of the fire element. The awareness of that feeling of lightness belongs to Nama and that feeling can only be experienced if attention is present and performing its mental function. Again, we see why attention can be included in the Nama-aspect.
So to answer the question: Attention
 is a mental factor. Mental factors belong to Mentality. Mentality is the Nama-aspect of Nama-rupa.

user10100: Citta and cetasica can not work their job without attention.
You can not know/memorize/feel anything, if you don't have attention on it. No one memorize stuff, that they never mind.
Full translation is:

Vedanā, saññā, cetanā, phasso, manasikāro — these (example of 53 lokiya-nāma) are called (53) nāma. 
The 4  mahābhūtā rupū  and (24) rūpā, that depend on mahābhūtā rupū,  — these are called (28) rūpa. 
These both, nāmā and rūpā, are called nāmarūpa.

Source:

Vedanā, saññā, cetanā, phasso, manasikāro - idaṃ vuccatāvuso nāmaṃ. Cattāri ca mahābhūtāni catunnañca mahābhūtānaṃ upādāya rūpaṃ. Idaṃ vuccatāvuso rūpaṃ. Iti idañca nāmaṃ idañca rūpaṃ - idaṃ vuccatāvuso nāmarūpaṃ.

So, nothing to doubt. Pali is clear.

user8044: There is this hierarchy in the teaching. One such is in the Nama…..  of the  rupa (material phenomena) & nama (mental phenomena).  Nama is broken down into Vedana (feeling) , Sañña (perception),  cetanā (mental activities),  Passa (contact) , and manasikāra (mental advertence). Buddha placed Passa & Manasikaara to the end for a reason. For the three things: feeling, perception and volition (vedana, sañña, and cetana) to be born contact must be there. Dependent on contact only manasikāra (mental advertence) happens. 
Vedanā, saññā, cetanā multiple series of mental events are rapidly arising and passing away from moment to moment. Only if contact happens -  Passa paccaya vedanā, saññā, cetanā….  with vedanā as condition, Tanhā arises.  Passa (Pāli) is a Buddhist term meaning "contact" or "touching”.  Dependent on contact only manasikāra (mental advertence) happens. 
In the case of an arahant the manasikāra is in accordance with the Dhamma. They live in the timeless present. For an Arahant in reference to the seen, there will be only the seen. In reference to the heard, only the heard. In reference to the sensed, only the sensed. In reference to the cognized, only the cognized. For him it is only “Passa”, whereas for you and me, it is ‘sampassa’ (san+passa). 
“San’ is basically the term for “good and bad things we acquire”. When we are thinking about an experience in the past or worrying about a future event, it all happens in the present moment. They are all activity of nāma-rūpa happening only in the present. From this ‘sampassa’ (san+passa) comes Ayonisomanasikāra.
Thus Manasikāra simply means ‘attention’. This in essence is the ability to be aware of the activity of the senses and the origin of mental phenomena, as it happens. The activity of the six senses. (1) Eye and forms (objects), (2) ear and sounds, (3) nose and odours, (4) tongue and tastes, (5) body and tactile objects, (6) mind and mental phenomena (mind objects). This happens both in you and me, as well as in Arahants.
In Arahants there is cetanā. In you and me it is san+ cetanā.  There is a distinction between sankhara and abhisankhara. Sankhara involves everything that we do to live in “this world”; these include breathing, walking, eating, etc. Even an Arahant has to be engaged in sankhara until Parinibbana or death. The prefix “abhi” means “stronger” or “coarse”. Sankhara become abhisankhara by engaging in the “wheeling process”. The sansaric process or the rebirth process is fueled by abhisankhara.

8157: <p>In respect to <a href="http://www.accesstoinsight.org/tipitaka/sn/sn12/sn12.002.than.html" rel="nofollow noreferrer">Dependent Origination</a>, the Pali suttas state: </p>

<blockquote>
  <p><em>Vedanā, saññā, cetanā, phasso, <strong>manasikāro</strong> - idaṃ vuccatāvuso nāmaṃ. Cattāri ca mahābhūtāni catunnañca mahābhūtānaṃ upādāya rūpaṃ. Idaṃ
  vuccatāvuso rūpaṃ. Iti idañca nāmaṃ idañca rūpaṃ - idaṃ vuccatāvuso
  nāmarūpaṃ.</em></p>
  
  <p><em>Feeling, perception, volition, contact and <strong>attention</strong> — these are called mentality. The four great elements and the material form
  derived from the four great elements — these are called materiality.</em></p>
</blockquote>

<p>Alternate translation:</p>

<blockquote>
  <p><em>Feeling, perception, intention, contact &amp; <strong>attention</strong>: This is called name. The four great elements and the form dependent on the four great
  elements: This is called form. This name &amp; this form are called
  name-&amp;-form.</em></p>
</blockquote>

<p>Why do we think 'attention' ('manasikara') is included within 'nama-rupa'? </p>

<hr>

<p><em>Note: I personally do not have a definite answer to this question, apart from personal speculation therefore I have asked the question for people to think about &amp; answer.</em> </p>
 8157: <p>Very good &amp; helpful answers, including @Saptha Visuddhi's reference to <em>ayonisomanasikāra</em>: </p>

<blockquote>
  <p><em>They are all activity of nāma-rūpa happening only in the present. From this ‘sampassa’ (san+passa) comes Ayonisomanasikāra.</em></p>
</blockquote>

<p>I was giving attention to this in meditation this morning and I decided upon this similar answer: </p>

<hr>

<p>Dependent origination arises from ignorance &amp;, of particularly relevance is, the absence of mindfulness &amp; wisdom at sense contact. About this, MN 38 states: </p>

<blockquote>
  <p><em>On seeing a form with the eye, he lusts after it if it is pleasing; he dislikes it if it is unpleasing. He abides with mindfulness of the
  body unestablished, with a limited mind and he does not understand as
  it actually is the deliverance of mind and deliverance by wisdom
  wherein those evil unwholesome states cease without remainder.</em></p>
</blockquote>

<p>In respect to this lack of mindfulness &amp; wisdom, AN 10.61 states:</p>

<blockquote>
  <p><em>Lack of mindfulness and clear comprehension, too, has its nutriment; it is not without a nutriment. And what is the nutriment of the lack
  of mindfulness and clear comprehension? 'Unwise attention,' should be
  the answer.</em></p>
  
  <p><em>When unwise attention (ayoni­so­ma­nasikāro) prevails, it will make prevail lack of
  mindfulness and clear comprehension.</em></p>
  
  <p><em>AN 10.61</em></p>
</blockquote>

<p>In summary, I think attention is included within nama-rupa because ignorance conditions/prepares nama-rupa for unwise/ignorant attention, which in turn will make sense contact unwise/ignorant. </p>
 -1: <blockquote>
  <p>Why do we think 'attention' ('manasikara') is included within 'nama-rupa'?</p>
</blockquote>

<p><em>Attention</em> is a mental factor (cetasika) that arises based on <a href="https://en.wikipedia.org/wiki/Mental_factors_(Buddhism)#Seven_universal_mental_factors" rel="nofollow noreferrer"><em>several other factors</em></a>, one of those being <em>intention</em> (cetana). It performs one of several cognitive functions that allows for consciousness of an object to arise. This can be experienced through the practice of insight meditation. As this is purely a mental function it is included in <em>Nama-rupa, i.e. the Nama-aspect</em>.</p>

<p>In walking meditation the meditator can experience the four great elements as actual processes (ultimate realities), e.g. the feeling of lightness that occurs in the lifting-phase of the foot. That right there is the experience of the fire element. The <em>awareness</em> of that feeling of lightness belongs to Nama and that feeling can only be experienced if <em>attention</em> is present and performing its mental function. Again, we see why <em>attention</em> can be included in the Nama-aspect.</p>

<p>So to answer the question: <em>Attention</em>
 is a mental factor. Mental factors belong to Mentality. Mentality is the Nama-aspect of Nama-rupa.</p>
 10100: <p>Citta and cetasica can not work their job without attention.</p>

<p>You can not know/memorize/feel anything, if you don't have attention on it. No one memorize stuff, that they never mind.</p>

<p><strong>Full translation is:</strong></p>

<blockquote>
  <p>Vedanā, saññā, cetanā, phasso, manasikāro — these (example of 53 lokiya-nāma) are called (53) nāma. </p>
  
  <p>The 4  mahābhūtā rupū  and (24) rūpā, that depend on mahābhūtā rupū,  — these are called (28) rūpa. </p>
  
  <p>These both, nāmā and rūpā, are called nāmarūpa.</p>
</blockquote>

<p><strong>Source:</strong></p>

<blockquote>
  <p>Vedanā, saññā, cetanā, phasso, manasikāro - idaṃ vuccatāvuso nāmaṃ. Cattāri ca mahābhūtāni catunnañca mahābhūtānaṃ upādāya rūpaṃ. Idaṃ vuccatāvuso rūpaṃ. Iti idañca nāmaṃ idañca rūpaṃ - idaṃ vuccatāvuso nāmarūpaṃ.</p>
</blockquote>

<p>So, nothing to doubt. Pali is clear.</p>
 8044: <p>There is this hierarchy in the teaching. One such is in the Nama…..  of the  rupa (material phenomena) &amp; nama (mental phenomena).  Nama is broken down into Vedana (feeling) , Sañña (perception),  cetanā (mental activities),  Passa (contact) , and manasikāra (mental advertence). Buddha placed Passa &amp; Manasikaara to the end for a reason. For the three things: feeling, perception and volition (vedana, sañña, and cetana) to be born contact must be there. Dependent on contact only manasikāra (mental advertence) happens. </p>

<p>Vedanā, saññā, cetanā multiple series of mental events are rapidly arising and passing away from moment to moment. Only if contact happens -  Passa paccaya vedanā, saññā, cetanā….  with vedanā as condition, Tanhā arises.  Passa (Pāli) is a Buddhist term meaning "contact" or "touching”.  Dependent on contact only manasikāra (mental advertence) happens. </p>

<p>In the case of an arahant the manasikāra is in accordance with the Dhamma. They live in the timeless present. For an Arahant in reference to the seen, there will be only the seen. In reference to the heard, only the heard. In reference to the sensed, only the sensed. In reference to the cognized, only the cognized. For him it is only “Passa”, whereas for you and me, it is ‘sampassa’ (san+passa). </p>

<p>“San’ is basically the term for “good and bad things we acquire”. When we are thinking about an experience in the past or worrying about a future event, it all happens in the present moment. They are all activity of nāma-rūpa happening only in the present. From this ‘sampassa’ (san+passa) comes Ayonisomanasikāra.</p>

<p>Thus Manasikāra simply means ‘attention’. This in essence is the ability to be aware of the activity of the senses and the origin of mental phenomena, as it happens. The activity of the six senses. (1) Eye and forms (objects), (2) ear and sounds, (3) nose and odours, (4) tongue and tastes, (5) body and tactile objects, (6) mind and mental phenomena (mind objects). This happens both in you and me, as well as in Arahants.</p>

<p>In Arahants there is cetanā. In you and me it is san+ cetanā.  There is a distinction between sankhara and abhisankhara. Sankhara involves everything that we do to live in “this world”; these include breathing, walking, eating, etc. Even an Arahant has to be engaged in sankhara until Parinibbana or death. The prefix “abhi” means “stronger” or “coarse”. Sankhara become abhisankhara by engaging in the “wheeling process”. The sansaric process or the rebirth process is fueled by abhisankhara.</p>
