Unpopular opinion:
I do not understand the hatred for the names Hadrian or Harrison as alternate names for Harry.
Maybe it's because I'm from the UK or maybe its because of where I'm from in the UK but I truly do not get the hatred and vitriol surrounding these two names. I've heard both of them in real life (mutual friends with 2 Harrisons also).
Looking at the wizarding world as a collective, the name Hadrian fits in very well. It's a name of an Emperor, it literally means "dark-haired" in Latin and it's got Roman origins (which we see frequently in the likes of Severus, Lucius ect) so for a son of a pureblood it's an understandable name, especially from a guy that has parents named Fleamont and Euphemia or Dorea and Charlus (depending on which lore you stick too).
As for Harrison, it's an old name dating back centuries meaning "son of Harry" and "son of the ruler" depending on where you're looking. The most common nickname is Harry and it got particularly popular when Harrison Ford shot to fame in '77 when a bunch of fans watched Star Wars and named their babies Harrison (as fans have done for years and still do today with whatever they love). So it's perfectly plausible that Lily, being muggleborn, decided she wanted to name her kid after a celebrity and James being in love with her enough just to be like sure.
Bare in mind, she was barely 20 when she had her baby and 20 years old (from experience) don't necessarily make the smartest decisions overall.
Plus, we see through out the series that characters get nicknames and have their names shortened all the time (Ron, Bill, Tonks, Charlie ect) so it's entirely plausible that Lily and James called their kid Harry shortening it like Molly does for all her children. And as we don't know how the story of the boy who lived actually got around it's very possible that they ran with the name Harry without knowing if he had a longer version of said name.
I digress, my point is: I don't get the sheer hatred for the names especially in a universe where there are characters unironically named Nymphadora, Quirinus, Bathsheda and so many others.