It often is a romantic gift, but I'm sad to say that it is not anything official. The star registry people maintain a database and sell you an entry in the database. It won't show up in any astronomical chart or registry used by scientists or astronomers.
I've been approached by many people asking me if I could show them the star they bought or received. Sometimes it would be a magnitude 14 star, which is impossible to see without a pretty big telescope. I have to admit being a little deceitful in some of these cases and move the scope to a nearby brighter star for them to look at.
Maybe Puritanboard should start selling stars. It would be just as significant and perhaps make better use of the money. I'd pick out good ones, but I'd also give full disclosure on what people are buying.