aight so uh... regarding the TL note at the end there: That's not much of a theory, it's kinda proven historical fact. Most early surnames for the commonfolk came from their professions or their parents. Smith, Tanner, and Baker are examples of the former, Johnson is an example of the latter. But many seen today have some deviation from their roots - Taylor from Tailor, Barker and Backer from Baker, Farman from Farmhand, Coleman from Coal man, and so on. And since back then many professions were passed down from parent to child,
Other surnames came from location, noble houses, or cultural exchange, people trying to transcribe illegible text as best they can, or people just not knowing how to read, pronounce, or spell their name or someone else's. An example of that last one is the legally blind Iditarod musher Rachel Scdoris - her surname was originally Sedoris, but a misreading changed the e to a c on an official document (IDR if it was a birth certificate or immigration paperwork) a few generations prior, and it stuck since nobody bothered to try fixing it.