My surname once broke authentication system behind my university. Any time I tried to login, it would crash for a few minutes logging out other users. Years later when I got my British passport it also contained my surname "latinised". I was told I should mail Home Office and get some certification that naturalisation certificates and passports don't include special accented letters and in fact the passport contains a mistake that cannot be corrected in the passport. Technically I have my Polish passport with different surname than the British one. This story isn't that unusual.
Also Polish, my pet peeve is having to write my latinised name into forms that specifically say "please enter your name EXACTLY like in your passport".
My pet peeve is online payment forms which ask to 'enter your name exactly as it is on the card' but require ASCII-only in that field - my name as embossed on the card has non-ASCII accented characters.
Anecdotally, it's slightly easier for Greeks and Bulgarians/Russians/etc. than for those of us whose languages use the latin alphabet with diacritics. The transliteration is generally standardised and English speakers tend to avoid even trying to use the other alphabet.
Pyotr Ilyich Tchaikovsky (note: Often anglicized as Peter Ilich Tchaikovsky; also standardized by the Library of Congress. His names are also transliterated as Piotr or Petr; Ilitsch or Il'ich; and Tschaikowski, Tschaikowsky, Chajkovskij, or Chaikovsky. He used to sign his name/was known as P. Tschaïkowsky/Pierre Tschaïkowsky in French (as in his afore-reproduced signature), and Peter Tschaikowsky in German, spellings also displayed on several of his scores' title pages in their first printed editions alongside or in place of his native name. The modern transliterations of Russian produce the following results for 'Пётр Ильич Чайковский' — ISO 9: Pëtr Ilʹič Čajkovskij, ALA-LC: Pëtr Ilʹich Chaĭkovskiĭ, BGN/PCGN: Pëtr Il'ich Chaykovskiy.)
I’m told today the transliterations are standardised enough that it doesn’t happen much. Greek and Russian friends describe less mangling of their names than I get.
Well, my Cyrillic full name has only two realistic transliterations, but I have friends who have it much worse. Especially people who has a Cyrillic Ë somewhere in their name, because it could be spelled without the diacritic in Cyrillic itself, leading to different transliterations.
Luckily I live in Armenia now, which not only has its own alphabet, but also has a tradition of armenising Slavic patronyms! (Which is fair, I guess, as Armenian patronyms are commonly russified in Slavic countries.)
Anyway, the transliteration of Cyrillic at least is not really standardised in my experience. It used to be worse, with Polish, French and English styles, now it settled on English, but there are a still several sticking points which cause combinatoric explosion of variants. Not to mention that my perspective is centered on Russian, and there is a different standard of transliteration for Ukrainian at least (Kyiv and Kiev are Levenshtein 2 apart in Latin, but Levenshtein 1 apart in Cyrillic), and there is a ton of other Cyrillic languages.
My perspective is on the experience of an immigrant in an English-speaking country. Greek and Russian friends give their standardised Latin-for-English transliterations everywhere and it works because there's no diacritics and no English speakers bother trying to read the Greek or Cyrillic versions. My own Romanian name being Latin alphabet with diacritics seems to get mangled in more ways, from what we've compared.
He's also Volodymyr / Vladimir, and it's like with Kyiv: the Levenshtein difference is increased by transliteration.
Also, I discovered that Levenshtein himself was from USSR, and that's why he's not Levenstein. Though I would not be surprised if some of his relatives would prefer Levenstein, just like Ekaterina (or Yekaterina?) Schulmann [1] doesn't like to be spelled as Shulman.
I don't think transcription from Greek is standardised. I've met several people "officially" called Vassilios or Vassileios or Vasileios or Vasilios while they were in the UK, but they all had the same name (Βασίλειος) in Greek, I think. I don't think the transcription of Russian names has been effectively standardised, either. I think I heard about a recent effort to standardise the Latin transscription of Bulgarian names, but that just suggests that they weren't standardised before then (or were standardised differently, at least).
Also, remember that it's Gorbachev in English, Gorbatchev in French, Gorbatschow in German, and so on, so there isn't likely to be a single Latin transcription unless it's one that's incompatible with existing usage.
Also note that it's usually "Rachmaninoff" in English, because he moved to the USA and became a US citizen at age 69, though you'd normally expect that name to be written as "Rakhmaninov" in English, I think; it's written "Rachmaninow" in German, for example. But that's an example of a different problem, really: people changing their names. While they're alive perhaps you might want to use their current official name, but when they're dead and if they're famous then you probably don't want to be forced to use the name that they adopted as a joke just before they died.
Names are not unique anyway. For most official purposes you should identify people with some kind of number and use the name as a check or to help a human sort things out when something doesn't match and you suspect that the number is wrong.
Today the transliteration of names is standardised, yes. You can ask for a different transliteration on your passport if you really want, but there is one official (sadly lossy) conversion table used for everything government-related, from people's names to street names. Street names in particular can get silly when we have a street named after a foreigner whose name is spelled phonetically in Cyrillic, but then is transliterated back into Latin, e.g. various things named after James David Bourchier are re-latinised as "Dzhejms Baucher"; "Dzheyms Bautcher"; or "James Boucher". Technically the first one is "standard". At least the boulevard bearing his name is now "James Bourchier" in Google Maps. Maybe one of these days they'll also support our addresses properly...
I am not sure about that part, iirc Bulgarian folks can pick how their name gets to be transliterated during the application for passport.
>English speakers tend to avoid even trying to use the other alphabet
Why care about English only, most of the Europe is not natively English speaking (save for the UK, Ireland and Malta) - the odds are the name are to be transliterated once to 'English', then pronounced in Spanish (think of the glorious H and J) or German (W vs V)
Mostly doesn't matter though, they sound entirely different compared to the letters without those changes. And you can't just replace them either, lots of words would suddenly have multiple meanings when written.