Your partner (fiance?) can legally adopt your daughter. In some states, though, your daughter's biological father would have to renounce paternity.
And, N., please, for your own sake, revise your post so it says the following:
"My baby is a little over a year old. My loyal, loving [boyfriend? partner? fiance?] functions as her father in every respect. Is there any way I can get his name on her birth certificate?"
People here can be terribly harsh about ungrammatical, confusing posts, particularly where they involve issues of uncertain paternity. If you want constructive advice rather than judgment, please take the time to make your post crystal-clear.