Genesis of name usage and evolution really can vary. Some is attributable to whether things were written down versus passed down orally versus skill or biases of transcribers. Indications are that my surname has its roots in Föhn Foehn of the Marshy Bog Leewards, and some branches went through all sorts of iterative transformations such as Fane, Vane, de Vaux, de Vallibus, Fen, Fenn, Fanning and I am sure others "happened." Much of it was toponymic, so changes were affected by what land was owned or a persons role in society.
As genealogists, we love to preserve accurate history, so the question might be best answered by what was the intent of the name user during their cohort, versus what we need to preserve about and "neatly categorize" as a historic reference. Having said that, I'll present you with this weakly-sourced report from Wikipedia:
When were surnames first used?
In Britain, hereditary surnames were adopted in the 13th and 14th centuries, initially by the aristocracy but eventually by everyone. By 1400, most English and some Scottish people used surnames, but many Scottish and Welsh people did not adopt surnames until the 17th century, or even later. Henry VIII (1491–1547) ordered that marital births be recorded under the surname of the father.
I got House of Habsburg https://en.wikipedia.org/wiki/House_of_Habsburg when I searched Hapsburg, too.
In today's headline in America: "Mueller names 'Hapsburg group,' reveals Manafort messages"
Sometimes, we have ethnocentrism that gets in the way: I primarily like to speak and write Queenglish; unfortunately, I only have high level fluidity in one language. That definitely will be off-putting and frustrating to some, if not many. On the other hand, if you ever met me and spoke with me, my language is very much less restrictive and less pedantic, and hopefully as easy, if not easier to understand as my written words.