Maybe the T was curious or asked you for the reason so that he could frame the answer in the context you wanted?

I wouldn't be ok with not getting a straight answer. It's your service/treatment, which they are getting paid to provide. Keeping you fully informed is part of their job. I think the DSM diagnoses are crap, but if one is being recorded in your record or sent to insurance, that's more the reason to ask what diagnosis is being used.

To not tell the client because a T suspects a client may have a sinister reason to ask for one is ridiculous. The client has a right to know no matter what reason they ask.