Which is interesting is
The first known use of Hapsburg was circa 1861
Just because English and German share a common spelling system (not completely, though), doesn’t mean words can’t be different. In English it’s still Cologne instead of Köln. In German it’s still Tokyo instead of 東京 or even just Toukyo.
I am German, by the way.
Generally, even without the counterexample, you just postulated an arbitrary, somewhat contrived rule. "Cities can have different names, people cannot, but only as long as the writing system matches". You can want this, but good luck with getting language to adhere to it.
If I'd correct Germans for all their "misuse", or at least idiosyncratic use, of English expressions (handy, public viewing, "learnings"...), it wouldn't make anybody happy. I put "misuse" in quotes deliberately, because German has just adopted these words into different meanings and connotations, just like Japanese did, and that's okay.
Language prescriptionism is not realistic.
Seems like a classic confusion about the difference between is and ought.
You believe that it should be obsoleted, but it is not obsoleted. Even the link you provided has no mention of the term Hapsburg being obsoleted, so I still have to wonder what you meant by "look it up".
You know how this works: human life is short, and our memory is even shorter, so it takes just one uneducated idiot to make a spelling mistake, then dozen of other idiots to repeat it, and after hundred years the mistake becomes a time-honored tradition.
Or to put it in tech terms: language is a blockchain.
Names often get switched around a bit when translated into other languages. If the Hapsburgs wanted to enforce a different spelling, I guess they should have built a better empire, haha.
Actually, no, usually they don't get "translated" to english if the name isn't written in an alphabet that needs transcription, like Cyrillic, Chinese, ...