No, but they do imply that when you name a star -- even though astronomers won't use the name you give it -- no one else will be able to name that star.

And, of course, even this tepid implication isn't true -- one person can name a star through starregistry.com, and another person can name the same star through starwishing.com. (And who knows how many other star naming "services" there are out there?)

In that sense, they do kinda-sorta imply "ownership" which isn't the case.