Psst.  Hey, kid.  Wanna name a star?  You can almost certainly get away with it, purely for your own and your loved ones’ entertainment purposes, whether it already has a name or not.  Property rights are not easy to enforce for gigantic plasma balls trillions of miles away.  Oh, you wanna name one officially, huh?  Who are you supposed to be — Barnard

If you’re not Barnard you should probably just go for it, and avoid stuff like this.

“There are still a few stars left to be named but you must act quickly to secure a good one before they run out.”

(emphasis in original)