Give the baby your surname only.

You are not married, and you are its mother and by the sound of it you already plan on having custody of this baby if the relationship doesn't last.

Do you really want to have a child with some ex partners name if you are later in a relationship where you want to take on the new man's surname? Then your child will not only not have your family name, but will not be able to have your new partners name.

WAY EASIER to just keep its name the same as yours until such time that the child can either choose for itself, or you know where you are going with a relationship etc.