Lots of hugs to you.
You're definitely doing the right thing to go back home. You'll need the support and help from those that are close to you.
A huge NO to putting his name on the birth cert. He definitely doesn't deserve to be in your life and your child's.
Personally I wouldn't concern myself with telling the gf about him. She won't believe you and he'll spin some lies that will make her believe them.
Best of luck and good wishes for you and your child's future!
Single mummy to a wonderful DS (Born 11/12/2008)