Children born to parents not married to each other.

The registrar of births shall register any child born to parents not married to each other at the time of the child's birth and where either the natural parents have not married each other or where the parent-child relationship has not been established pursuant to chapter 584A, as having both a family name and given name chosen by the individual who gave birth to the child, unless the child is born to a gestational surrogate or genetic surrogate pursuant to part IX, in which case, the child's name shall be chosen by the intended parent or parents.