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 assumption

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).