When future parents have a child through surrogacy, they need to accomplish two goals: the first is to ensure the surrogate does not have rights as a parent to the child. The second is to ensure a partner who is not biologically related to the child can become recognized as a parent to the child. What dictates how easy or hard this is to accomplish is the state where the surrogate lives and gives birth.
Some states make this process incredibly easy, and selecting a surrogate who lives there is a good move. Those states are California, Connecticut, Delaware, Oregon, New Hampshire, New York (as of April, 2020) Maine and Nevada. Here, paying a surrogate to carry a child is legal, and it’s easy to have both parents placed on the birth certificate a priori. Typically, surrogates who live in these states are able to command higher rates because there is a lower risk that they can complicate matters legally.
On the other hand, nobody pursuing surrogacy should consider doing so with a surrogate living in Louisiana or Michigan, as examples. In these states, it is illegal to pay for a surrogate to carry a child, and so the intending parents have virtually no rights and are completely exposed should the surrogate want to keep the child.
In the other remaining states and territories, the rules can vary case-by-case, and county-by-county, with varying degrees of precedent and certainty. Surrogacy may be permitted, but ensuring the non-biological father can be readily recognized as a parent may be cumbersome.