How to cite an author who spells his name inconsistently

The decision will in the end rest with your publisher, so I suggest you address the question to your editors—that’s what they’re paid for, and they will probably appreciate your calling their attention to the problem. In fact, the standard authority in my own field, MLA Style Manual and Guide to Scholarly Publishing, although it does not directly address this question, does say of spelling variants in general that you should “inform your editor, before copyediting begins, of any necessary deviations” from the practices MLA otherwise recommends. (3.4.1)

MLA also says “If the name of an author whose works you used appears in various spellings in the works (e.g., Virgil, Vergil), consolidate all the entries for the sources under the preferred variant in your works-cited list (6.4.3),” and it specifically distinguishes this from the need to list separately works written under natal and married names.

My reading of these suggests that you employ the version with the ‘long’ umlaut throughout, with a note at each relevant works-cited entry of the variant spelling under which it was published.

And Oh, yeah: in the works-cited list (but not the body of your text) Prof. Szegő should appear as Szegő Gábor, with no comma: Hungarian, like many East Asian languages, puts the surname first.