I was born in Latvia, which at the time was a part of the USSR. My birth certificates are in Russian, and my name in Cyrillic is Артем Шинкаров. Its correct transliteration is Artem Shinkarov.
Unfortunately, in my passport, my name is transliterated as Artjoms Šinkarovs. Mind extra s-es at the end, jo in the middle and Š instead of Sh. This is something I cannot change due to crazy Latvian rules.
In the UK, my name got transliterated again, simply by throwing away the diacritical symbols; so I ended up with Artjoms Sinkarovs.
While Latvia recognises that the transliteration mismatch is a problem, no proper solution has ever been implemented. It is possible to put the correct spelling of your name in the passport, which I surely did:
However, turning this spelling into the official one, in all the documents, is a total nightmare.