Birth State Vs Conception State

My daughter lived with her boyfriend in TX and got pregnant. She is 6 months into the pregnancy and he has now told her he wants nothing to do with the situation and told her to leave their home (rented under his name). She is temporarily staying with her mom in TX but wants to come to MO and live with me and get away from it all. Several questions:

1) does she need/have to name the father on the birth certificate (regardless of where the child is born)?

2) does the child have to have the same last name as the father or can she give the child her last name?

3) if the child is born in MO, she lives in MO and the father lives in TX does she file for child support in MO or TX?

Any assistance/advice I can give my daughter is much appreciated!!!