Let him get a paternity test, if you ever need to go after him for child support then you'd already be one step closer in case he wants to deny the child is his. You can still name the baby after you, a DNA test has no effect on that, it's up to you no matter what :) At least here in the US, if you're not in the US you may want to check
You can ask if he has any rights for a DNA test regarding your situation, but as for the last name, that's your decision.
So he don't have any rights when it come to that.
Just because he gets a DNA test done still doesn't make it required for your baby to have his last name. It's not required so don't worry about it and good luck with the rest of your pregnancy