These names are now "English", and their spellings are pretty standard - in particular the "c" spellings are established.
Since essentially everyone uses "dodecahedron" rather than "dodekahedron" or "dodecaedron", this really forces the spellings
octagon rather than oktagon
hendecagon rather than hendekagon or endecagon
and so on.
However, there IS some point to having a standard transliteration system from languages which don't use our alphabet. I found this when I was involved in translating Russian mathematical papers into English - The American Math Soc has such a standard system, and it's very convenient - different translators will use the same trasnliteration, and the transliteration has the great advantage of determining the spelling of the original. These advantages compensate one for the fact that some names that already have standard English forms appear in unaccustomed versions.
Of course, we've all seen this in far Eastern names, like
Beijing, Myanmar, etc. We'll get used to them.
About changes in German spelling:- As well as the change from c to k, in the late 19th century, "th" was simplified to "t".
So the verb "thun" (to do) has become "tun", and "Thur" (tower) has become "Tur", while "Thal" (valley) has become "Tal".
Some well-known proper names that were Englished before this change retain the "th" - eg "Rosenthal", "Winterthur", and one of these has become an English adjective: "neanderthal" (although I gather that some paleologists now prefer "neandertal").
My own feeling is that once a word has gone so far as to lose its capital letter, its English spelling is best kept fixed. But otherwise, we should usually "do as the Romans", except in a VERY few well-known cases. So for example I'd use "Rome" rather than "Roma", but "Hannover" rather than "Hanover", and maybe "Firenze" rather than "Florence".