user23535: If reincarnation were true, in that a soul takes on different human bodies across several different lives during that soul's existence, have philosophers, theologists, scholars or any scriptures ever indicated whether one of those lives is the true identity of that soul? Or is it implicitly always assumed that the first life or incarnation of that soul is its true identity?

user471: I can't offer you the Jewish yarmulke, but I can try to explain the Buddhist Yamaka. The Yamaka Sutta is one of the texts you can read. There are more in this answer. Another one is the Vina Sutta.
Let's take the example of someone called George, whose mother has now passed away.
George knew his mother since he was a child. Then she was young and energetic.
As she grew older, her body and appearance changed. She then has wrinkles and white hair. She had trouble walking long distances because her legs weren't what they used to be. Her outlook of life and her opinions have changed. But she's still his mother.
Then in her very old age, George's mother became senile, experiencing dementia. Now she could not recognize George anymore. Her personality had changed drastically. Even George couldn't recognize her personality anymore. But she still looks like his mother and George hopes that "she is in there somewhere".
Then one day she died. George looked at his mother's dead body and cried, "Mother, why have you left me?" Although the body is there, he thinks his mother has left him. Why is this the case? Does he think his mother is not the body? Then what does he think his mother really is?
When they had a funeral service for his mother, George looked at his mother's body in the casket, and said "Goodbye Mother, I love you." So, now he thinks the body is the mother?
Long after the funeral, he reflected that when she became senile, it was like she wasn't there anymore. George thought, "Mother really left me a long time ago."
Later, after a year, he has a new daughter born to him, who looks and behaves a bit like his deceased mother. George wonders, "could my mother have been reborn again to be my new daughter?"
So, who really was his mother? Was she the form (body)?  Was she the feelings (sensations)? Was she the perceptions (including memory)? Was she the consciousness? Was she the mental formations (including personality)?
Or was she none of these? Or all of these in combination?
If you remove each of these one by one and examine it, would you find the mother?
What was her true identity?
Form, feelings, perception, consciousness and mental formations - these five aggregates are all impermanent (anicca), unstable and unreliable.
It's just like the case in the Vina Sutta where the king broke a lute into its constituent parts to find the melodious music that it produced. He couldn't find it.
Even in this very life, it's hard to pin down exactly the true identity or the true self. In this case, how would it be possible to pin down exactly the true identity or true self across multiple lives?
The Buddha taught that "all phenomena is not self" (sabbe dhamma anatta). If you look for the true identity or true self, you will find that there is none.
Also, please read this answer, this answer and this answer.

23535: <p>If reincarnation were true, in that a soul takes on different human bodies across several different lives during that soul's existence, have philosophers, theologists, scholars or any scriptures ever indicated whether one of those lives is the true identity of that soul? Or is it implicitly always assumed that the first life or incarnation of that soul is its true identity?</p>
 471: <p>I can't offer you the Jewish <a href="https://en.wikipedia.org/wiki/Yarmulke" rel="nofollow noreferrer">yarmulke</a>, but I can try to explain the Buddhist <a href="https://suttacentral.net/sn22.85/en/bodhi" rel="nofollow noreferrer">Yamaka</a>. The <a href="https://suttacentral.net/sn22.85/en/bodhi" rel="nofollow noreferrer">Yamaka Sutta</a> is one of the texts you can read. There are more in <a href="https://buddhism.stackexchange.com/a/45337/471">this answer</a>. Another one is the <a href="https://www.accesstoinsight.org/tipitaka/sn/sn35/sn35.205.than.html" rel="nofollow noreferrer">Vina Sutta</a>.</p>
<p>Let's take the example of someone called George, whose mother has now passed away.</p>
<p>George knew his mother since he was a child. Then she was young and energetic.</p>
<p>As she grew older, her body and appearance changed. She then has wrinkles and white hair. She had trouble walking long distances because her legs weren't what they used to be. Her outlook of life and her opinions have changed. But she's still his mother.</p>
<p>Then in her very old age, George's mother became senile, experiencing dementia. Now she could not recognize George anymore. Her personality had changed drastically. Even George couldn't recognize her personality anymore. But she still looks like his mother and George hopes that &quot;she is in there somewhere&quot;.</p>
<p>Then one day she died. George looked at his mother's dead body and cried, &quot;Mother, why have you left me?&quot; Although the body is there, he thinks his mother has left him. Why is this the case? Does he think his mother is not the body? Then what does he think his mother really is?</p>
<p>When they had a funeral service for his mother, George looked at his mother's body in the casket, and said &quot;Goodbye Mother, I love you.&quot; So, now he thinks the body is the mother?</p>
<p>Long after the funeral, he reflected that when she became senile, it was like she wasn't there anymore. George thought, &quot;Mother really left me a long time ago.&quot;</p>
<p>Later, after a year, he has a new daughter born to him, who looks and behaves a bit like his deceased mother. George wonders, &quot;could my mother have been reborn again to be my new daughter?&quot;</p>
<p>So, who really was his mother? Was she the form (body)?  Was she the feelings (sensations)? Was she the perceptions (including memory)? Was she the consciousness? Was she the mental formations (including personality)?</p>
<p>Or was she none of these? Or all of these in combination?</p>
<p>If you remove each of these one by one and examine it, would you find the mother?</p>
<p>What was her true identity?</p>
<p>Form, feelings, perception, consciousness and mental formations - these five aggregates are all impermanent (<em>anicca</em>), unstable and unreliable.</p>
<p>It's just like the case in the <a href="https://www.accesstoinsight.org/tipitaka/sn/sn35/sn35.205.than.html" rel="nofollow noreferrer">Vina Sutta</a> where the king broke a lute into its constituent parts to find the melodious music that it produced. He couldn't find it.</p>
<p>Even in this very life, it's hard to pin down exactly the true identity or the true self. In this case, how would it be possible to pin down exactly the true identity or true self across multiple lives?</p>
<p>The Buddha taught that &quot;all phenomena is not self&quot; (<em>sabbe dhamma anatta</em>). If you look for the true identity or true self, you will find that there is none.</p>
<p>Also, please read <a href="https://buddhism.stackexchange.com/a/45337/471">this answer</a>, <a href="https://buddhism.stackexchange.com/a/25302/471">this answer</a> and <a href="https://buddhism.stackexchange.com/a/39742/471">this answer</a>.</p>
