There are no possible problems that can arise from the baby having the last name of the child's father as opposed to the mother.
Shoot, the child could have my last name and never incur a problem. No one cares what you name your child these days. What kind of problem do you think there could possibly be?
Think of it this way... darn near 60% of marriages fail. Lots of those marriages produced children. Those children have the last names of their fathers, and a percentage LIVE with their mothers. The mothers remarry, and her name changes. Now, those children don't have their mother's last name either. You think they grow up having a bunch of problems?

