Sounds like that guy was looking to cheat, he went on Grindr to hook up and messaged you; you didn't make him cheat by not asking if he was taken. I'd be angry, if anything, in your shoes. But you're not the guilty party here.

Your gf is being straight up disrespectful; calling someone by a new name isn't hard and changing your name doesn't change who you are. There's probably a bigger issue here she's refusing to address and hiding it behind the name, but the fact is this is important to you, you communicated it clearly, and her blatantly refusing to respect your wishes is a major red flag. If she can't support this small change, how will she support your career in the long run? What else is she willing to steamroll in your relationship? Obviously I don't know your life but, having changed my own name, the people who couldn't deal were always the ones best left behind.