Need some advice.

So I'm pregnant. I'm not with the father because he caused me domestic abuse. I'm hoping to take him to court to take out an injunction. I'm seeing someone else, someone that I've known for quite a long time. My current partner is willing to stick by me throughout everything. The pregnancy, the scans and even the birth. I've been speaking to him and his mum about the whole situation. His mum made a comment saying 'you've got to make a decision on what your baby will call him. Will it be by his real name or will it be daddy' I didn't even think about this beforehand. The real dad will not be much of a dad because he's more interested in drugs, alcohol and knifes and I personally think he will get bored. Whereas my current partner seems so involved with everything even though the baby isn't actually his. What would you do in this situation?