Probably. If they don't ID themselves, how can you even know they are citizens?
We have the right not to testify against ourselves, I'm not sure we have the right not to even ID ourselves.
I believe the US Supreme Court recently declined to overturn a decision that upheld the arrest of a citizen for failing to provide ID.
Maybe their names are incriminating, as with the guy who did identify himself.
If so, they have a Fifth Amendment right to remain silent. However, in order to prove that they do have such a right, they'll have to reveal their names.