Directly from a Minnesota law web site:
Minnesota law automatically presumes that a husband is the "legal" father of a child born to his wife during the marriage. If a woman is married and has a child by someone other than her husband, Minnesota law automatically presumes that her husband is the father and he will be legally responsible for the child UNTIL paternity is established with the other man. The biological father has no legal rights or financial obligations to the child, UNLESS he is established to be the "legal" father."
I would probably not give the baby the biological father's last name until and unless you're completely remarried to him. I would give the baby YOUR last name. If you're completely certain that this other guy is the father and your husband is not, you could give the baby the other guy's surname as the baby's middle name, but I would make the official surname YOUR surname.