My name on transcript has no surname. Should I list it as a "former name" when applying for universities in U.S.A. and Canada? I'm in the process of applying to graduate schools in U.S.A. and Canada as an international student and run into this issue:
The name displayed on my passport and national ID consists of first name, middle name, and family name. However, on my transcript, my family name is not shown. I presume that this makes a difference. 
Some of the universities' registration page has fields for former name(s) listed on previous records/certificates. Should I indicate the name on my transcript in the former name fields since it lacks the family name while the one on my passport has my family name?
In addition, should I make an affidavit letter to state that the name on the passport and the transcript belong to me?

About on how I ended with only my first name and middle name on my transcript:
In my country, as far as I know, the way the name is put on every academic record must be the same as the one on those preceding them. Also, it's usual here to write the only the given name in full and either omit the surname or make an initial of it if the space permits since many ethnic groups here do not actually use family names. I have many friends at college who did not use their surnames for their records. Back to academic records, my name has been written without a surname in academic records since elementary school, when my dad did the application process.
It sounds like the forms you have been provided already give a sufficient means of clarifying, particularly you indicate the form is specifically meant to link a current full name to an alternative shown on formal records.  While the university may have been thinking about different cases, like names changing via marriage, it fits your situation as well.

I would suspect getting an affidavit or other formal attestation is not necessary: if they are not asking for it in the other cases where a name does not match, they should not expect it for your case either.