>> Try to interact with the Greek government and they might ask you to spell your name using only their characters. An interesting challenge when your name contains sounds that don't exist in the local language (sh, hu).
Seen from the other side, a friend of mine called Γωγώ (short for Γεωργία, i.e. Georgia) spelled her name "Roro" when she went to France. The standard transliteration would be "Gogo" but the French would pronounce that like "go-go", whereas they pronounce the "R/r" like Greeks pronounce the "Γ/γ".
And how about all the Greek women who take on their father's spelling of the family name in English-speaking languages (as have I)? E.g. Olympia Dukakis: that's a male form (Δουκάκης); the female is "Doukaki" (Δουκάκη). But, try to explain that to speakers of a language without grammatical genders. Sounds more like a spelling error.
I understand that Icelanding families have a similar problem, with surnames that name the parent, so that if the father's first name e.g. Bjorn, the son's surname would be Bjornsson and the daughter's name would be Bjornsdottir, with the father and mather's surname being whatever -son or -dottir reflects their ancestry. Can cause trouble when going through passport control as a family with underage kids all with different surnames.