Hi, answers might depend on your system / OS / apps / printer models...
In Windows land all ICC profile files end up in C:\Windows\System32\spool\drivers\color. I dunno whatsit in Mac land. If they're in there and you didn't add them yourself manually then some app added them. You can delete them if you want, but it's possible that app will put them back again later.
ICC profile files have an internal description field, which is what is displayed in apps. You can see it by opening one in a text editor, it'll be near the top. Unfortunately the description name often doesn't match the filename. I think there are ICC file tools out there that let you change those descriptive names..., I've probably used one but can't recall what right now.
Adding/deleting ICC files should be reflected in apps like Photoshop the next time you start them.
I occasionally prune ICC files if I know where they came from and I don't need them. Usually it's outdated profiles that I made myself. But leaving them there doesn't really hurt anything, they just make the list longer to scroll in apps.