Can your boyfriend adopt your 16-year-old daughter and place his name on her birth certificate without the consent of the child's biological father?

The biological father would have to voluntarily relinquish his rights or the court would have to terminate his parental rights to the minor child before the child could be adopted by anyone.

FYI, in most cases the "boyfriend" could not adopt the minor child even if the biological father were to give up his parental rights. The mother of the child and her significant other generally have to be legally married before the court would allow an adoption to proceed. This mostly depends on whether your state recognizes your union in some way (some sort of civil union). Occasionally, some odd exceptions are granted (in Alaska, there was a petition where a 3rd person wanted to legally adopt a child, and the court granted it)