How to deal with inconsistencies in my last name spelling on official documents? In my native language, my last name contains a letter, which can be transliterated into English in three different ways. Namely: ja, ya and ia. When I tried to transliterate my last name to English for the first time, I checked the results of several online translators, and they all transliterated  my last name to English with ya. I kinda liked that option as well and decided to stick with it.
After some time, I was issued my first passport, and it contained the other variant. I didn't want to drop my initial choice, because I liked it more and didn't want to rename all my Internet accounts either.
Yesterday, I had gone to a translator agency to translate my transcripts for the Master's program application and the translator asked me to write my last name exactly as in my foreign passport. I have realized that I have a lot of documents with the initial variant variant, which can't be reissued. For instance, all my award certificates and TOEFL results. Now I'm going to change everything I have to make consistency with my foreign passport, as it might cause problems with visa issuing.
I have two questions:

How I should cope with documents with the old last name option, which can't be reissued?

I think one way would be to add a footnote in my CV (which contains links to all certificates) which will notify the referees that I have written my last name previously in a different way.

Do you think that referees of Master's program admission might invalidate my TOEFL results because of this inconsistency?
I think this problem is widespread enough that it shouldn't be a problem, provided that you make people aware of it. You suggest a note in your CV and that should be fine. It could appear elsewhere also.
If you are questioned on it or someone makes a mistake in thinking you are acting improperly, just inform them of the issues. I think people will, in general, try to be reasonable, though I can't predict for everyone.
I know one person who immigrated to the US from China. His brother did also a bit later. They have &quot;different&quot; family names when written in Roman letters because of this issue. Most English speakers even pronounce the names a bit differently now. My own family name is spelled in at least three different ways in the US because my ancestors coming from Ireland were illiterate on arrival and people wrote down a spelling for them when they arrived based on pronunciation.