I am writing a paper where I will cite several works by the Hungarian mathematician Gábor Szegő. Note that his surname includes the letter o with a double acute accent, NOT a letter o with umlaut ö. In his first paper (that I know of) he spells his own name this way, and biographies of him always use this spelling.
However, in later works (such as a major book that he published) he usually uses an umlaut for his name instead. I am not sure whether this is because of technical limitations on what accents could be typeset at the time or because he moved out of Hungary (which did happen) and was trying to spell his name in a more appropriate way. Additionally, a theorem has been named after him (which is a great honour for a mathematician), but it is usually spelt as the Szegö limit theorem with an umlaut.
Should I follow convention with the theorem name or try to correct it by using the original spelling of his surname? And how should I cite his work? To clarify, I am of course asking whether there is an accepted convention on such things, rather than looking for opinions on what people would prefer that I do. Unfortunately I plan to cite both his original paper and later book, so if I cite his name in the way it's spelt in the work then I'll have Szegő and Szegö right next to each other in my bibliography! And if I use author-year citations then I'll have them right next to each other in my text (see Szegő, 1915; Szegö, 1952)!
(Thanks in advance for any help. Apologies if this is not the right place for this question. It applies equally in any language, but this seems the most appropriate StackExchange board.)
Edit: I should point out that the 1915 article isn't written in English (nor Hungarian: it's in German). It seems that all of Szegö's work in English used the umlaut, so perhaps he considered it to be the correct way of writing his name in English. Just as we have Pythagoras's theorem rather than Πυθαγόρας's theorem and Sobolev inequalities rather than Со́болев inequalities, perhaps Szegö is always (and only) correct in English.