What did he say?

You've obviously never read Christine.

Christianity is a religion. People who follow Christianity are called Christians. Christian is also a fairly common male name in English speaking countries. At first, when the girl in this scenario told the guy she used to be Christian, he assumed she was talking about the former definition. He is then informed that she was in fact talking about the latter definition, and changed her name to Christine, which is a common female name. This is a bait and switch. The reader initially assumed that this was going to be a joke about religion, but it turned out it was a trans joke.

The joke would be a lot less funny if it went like this:

I was on a blind date with a woman, and during our dinner conversation....

....she said, "You know, I'm trans."