I don't really see Tim calling himself Tim Wayne as a disrespect to his parents. I see it as his way of showing that he belongs as part of the family. He's had two dads die now, and Damien is being a little shit telling him to get lost and that he is not welcome. Dick has the cowl, and Damien has the name AND the Robin suit, maybe Tim sees taking the name as the only thing he has left of Bruce and the family.
I wonder if there is any way to ship Damien back to Talia?