Am i required to put the fathers name on the birth certificate if we are unmarried and not together. Also who has primary custody.

If there has been no naming of a father at the time of birth, and no court action regarding paternity, then under NRS 125C.003: 2.  A court may award primary physical custody of a child born out of wedlock to:       (a) The mother of the child if:                (1) The mother has not married the father of the child;                (2) A judgment or order of a court, or a judgment or order entered pursuant to an expedited process, determining the paternity of the child has not been entered; and                (3) The father of the child:                      (I) Is not subject to any presumption of paternity under NRS 126.051;                      (II) Has never acknowledged paternity pursuant to NRS 126.053; or                      (III) Has had actual knowledge of his paternity but has abandoned the child.         (b) The father of the child if:                (1) The mother has abandoned the child; and                (2) The father has provided sole care and custody of the child in her absence. It is probably a good idea for you to review the rules applicable to child custody, and child support, both of which you can find and review here.