If mom is amenable and there is NO FATHER listed on the birth certificate, all you have to do is both parents go to the local health department and swear out an affidavit of paternity. You can then mail this off to the Vital Records with the fee and they'll amend the birth certificate (with the new last name).
If all of the above is not true: i.e., mom isn't cooperating, there is some other person listed on the birth certificate, etc... You'll need to apply to the JDR court for this (it would behoove you to have established paternity).

