"In Jesus Name" is a STANDARD closure to any Christian prayer and has nothing to do with "emphasizing differences".
If you are my guest, say, and I make a small toast, and say: "In the name of proletarians and communist of the wordl, let's drink to the future" --- you would be appalled. You would say, "Don't take me in your company; believe in whatever you want but don't take me in your company." I would reply, "That is the standard toast at communist meetings and has nothing to do with differences."
You would call my argument stupid. And you would be right.