Should his name be on baby shower invite?

My child’s father received an invitation for my baby shower (that my mom is throwing) his name was not included on the invite. He is upset because his name is not on the invite. He does not live in the same state as me. My whole pregnancy he has only sent me $20 despite blowing money on trips and Alcohol while ignoring my calls/texts about appointments.

He texted me and said “If I come can we place my name on the invitation?”

The baby shower is going to happen regardless of whether or not he comes so...