“I don’t attend services under that denomination”
So where DID you attend?
The name of the church I attend is (unfortunately for you) specific enough in name, that IMO neither you nor the government have any legitimate need to know.
But let's assume that you had a need, for the sake of argument. You know the creed that I profess. What specific, additional value would the name of my church pass on to you, given that you already know WHAT I believe?