In Ashkenazic practice (Jews of Eastern European origin), the custom is to name a child after a relative who has died, while Sephardim (Jews of Spanish and Middle Eastern origin) tend to name their children after living relatives. Reform practice allows either option. Jews-by-choice certainly may name their children after their parents, since Jewish tradition recognizes that all people, including people who have gone through conversion owe honor and respect to their parents.
Source: Rabbi Mark Washofsky, Ph.D., Jewish Living; A Guide to Contemporary Reform Practice (URJ Press, 2010).
See also: What is Pidyon Haben?, B'rit Bat: Ceremony for Welcoming a Baby Girl, B'rit Milah: The Circumcision Ritual, How To Find the Right Mohel For You.