Most do. The local indoor range I go to requires ID and photocopies it.
My member-only gun club has sign-in sheets, and it’s a revocation offense to fail to do so.
We have a gate with a code. But it’s a universal code, so they cannot tie it to me as an individual. I had to provide my information when I joined years ago, but I don’t have to do it when I go. I will admit that when I go, there is often no one else there.
And this is in MA.
I know at some indoor ranges they are much more strict. But those are in the city and they need to avoid the local gangs from “training” there.