Most interesting case I've come across was a guy who just had one name. No surname or anything. He was once questioned by police (regarding a theft in the shop he worked in) and explained that his parents were "a bit weird". He was originally American, so apparently that's also a possibility there? And apparently the Dutch system allowed it, although the police seemed to struggle with it and may have duplicated his name.
It can go the other extreme too of course: https://www.stuff.co.nz/nz-news/360848808/worlds-longest-nam...
source: gave my children fancy names
Some US bureaucrats seem to like FNU (First Name Unknown) or LNU (Last Name Unknown). So one encounters mononymous Americans whose first name is Fnu or last name is Lnu. A while back I had a coworker whose surname was Fnu – I believe her legal paperwork had Fnu as her first name, but she got IT to swap her firstname and lastname in our corporate systems, because she didn't want people addressing her as Fnu.