Dad not being involved

Hi,

I want my child to have both our last names as I have been with dad far less than a year but he said if it has my last name I will be bringing it up alone. He accuses me of cheating everyday and says the baby isnt his (never happened and isnt possible). We just bought a house together but he keeps threatening to do things to himself and not be involved with the child till it is 18. He tries to blackmail me into having sex and always uses not being involved with the baby as a threat. What do you think I should do? Do you think I should stay and put up with it? (We just bought a house together