I was surprised to learn here that the man responsible for "König's Lemma" was Hungarian, and spelled his last name Kőnig (with a different accent on the o), presumably with the same accent that occurs in Paul Erdős' last name. I still remember being taught that this accent was not an umlaut, and had a special LaTeX command.
Now, in the Konig-case, what adds more to the confusion is that we mathematicians historically have used the (incorrect) umlaut spelling when referring to the the tree lemma. Moreover, Kőnig's father apparently spelled his name with an umlaut (according to a comment by Asaf Karagila here).
Should we as a math community correct the spelling of "König's Lemma" to match the name of the one honored by it?
Edited to add: The story gets even weirder. Kőnig sometimes spelled his name (or, at least, the editors spelled his name) as König in some of his publications. For the 1927 publication in question, the marking on his name, on the first page, is hard to make out, but appears to be the Hungarian marking. But on the running header throughout the paper, the markings are clearly the German umlaut!