publications - How to prove that a paper published with a particular English transliteration of my Russian name is mine?

My first name is Евгений (it is Russian; the usual transliteration is Yevgeny). I was born in Ukraine in 1990, when it was still in the Soviet Union, where Russian was the official language. I lived there until 2011, when I went to Canada, where I am currently working on a Ph.D in mathematics. The name indicated in my passport is IEVGEN. It has undergone two rounds of changes: first it was translated from Russian into Ukrainian (Евгений => Євген), and then the Ukrainian version was transliterated into English under the transliteration rules that were valid at the time of receiving the passport. If I received the passport under the present rules, it would be spelled as IEVHEN. The issue here is that the sound in the Ukrainian version is something in between of G and H.

I am deeply unhappy with the "name" IEVGEN: it looks odd, it is not pronounced as the Ukrainian version, and it is definitely not how my parents named me.

I really don't want this spelling to appear on my publications, and ideally even on my Ph.D. thesis. Right now I don't know which version I would prefer, but let's consider YEVGENY, which is the closest to the original, and EUGENE, which is the English/French version of the same name. I know that I am the one who decides under which name to be published, but it raises the following question:

If at some point I will need to prove the authorship of a certain publication that bears a name slightly, or significantly different from what is in my documents, will that be a problem?

EDIT: some of the answers suggest me several ways of how to spell my name, and I appreciate them, but it is not what I have asked. My question only had to do with bureaucratic and juridical aspects of the problem.

EDIT 2: The title of the question was changed by an editor to "What author name to list on publications when English translation of Russian name on passport is unsatisfactory?", which is again completely misleading. I am not asking what to put on publication, I am asking about how to prove that the chosen name corresponds to me. So I edited the title back to the original.

Answer

As a possible solution if you are still worried about it: Get an ORCID account.

They basically created an ID, a DOI for researchers. If you link your publications to your ORC-ID, you don't need to worry if your name is very common (e.g. John Smith) or if someone misspelled your name.