No, you do not have to agree to ANY of his requests, and if the facts are as you suggest, he will not succeed on any of those claims over your objection. As to the name issue, there is one leading case:
Magiera v. Luera, 106 Nev. 775, 802 P.2d 6 (1990)
Out-of-wedlock child; district court's order to have dad's name put on birth certificate reversed where parties had never been married, dad did not pay support until wages garnished; only question is best interest of child; dad not entitled to "tangible benefit" for finally paying support; burden is on party seeking name change to prove by clear & compelling evidence that the substantial welfare of child necessitates a name change.
As to taxes, the analysis is much the same -- you presumably are providing the bulk of the child's actual support, and are therefore entitled to retain the tax benefits. For background, see the Child Custody page of our firm website, at http://www.willicklawgroup.com/child_custody_visitation.
You should probably seek consultation with an appropriate family law specialist. If you would like to discuss this with one of the attorneys of this firm, please take a look at our consultation policies, procedures, and costs, at http://www.willicklawgroup.com/consultation_policies.