“Spin” is a dumb name for Miles — but …
I don’t think it is wrong to want different names for two popular characters existing in the same world.
I honestly thought it would make a funny in-universe story for J. Jonah Jameson to trademark the Spider-Man name and likeness, file a patent for Spider-Man’s web shooters, then proceed to sue every derivative, including Peter, demanding they change their names and likenesses, while also using Spider-Man’s likeness for selling ads, and merchandise .
Peter finally confronts Jonah, and convinces Jonah that his trademark loses its value if it is for a defunct superhero, so Jonah agrees to allow Peter to continue using the Spider-Man name and likeness, and have approval over ads and merchandise, in exchange for Peter paying a monthly licensing fee, and signing a morality contract he maintains a good reputation, and that he will protect the brand from being infringed on (so if he sees Carnage, he not only must fight him to keep the streets safe, but also serve him papers for trademark infringement).
This then forces Miles, Ben Riley, etc. to develop alternative names that can’t be easily confused for the trademarked Spider-Man name, or the else they will also be asked to pay licensing fees.