J.B.
You can do a person search-
freeality.com has good links for that
and to change your daughter's last name you will need to look into your local courthouse for the paperwork required. If dad has gone MIA you may
be able to petition the courts on the basis of him disappearing, and potentially start a case against him to collect on back-owed child support payments. I would also look into how to get him to terminate parental rights.
http://www.namechangelaw.com/states/nc/northcarolina.htm
Good luck!