Github lets me name my passkeys. There's a little pencil icon next to each one (on [1]), and as far as I remember it even prompted me for a name when I originally created it.
There does seem to be some way. I'm relatively sure I've seen keys pre-labeled with the name of my password manager in the past.
Some sites make bad assumptions, though, e.g. labeling every passkey I create as "iCloud Keychain" (because my user agent tells them I'm on macOS, and they assume that it must be that then).
[1] https://github.com/settings/security