The fee you pay the domain name registrar is an annual fee. In other words, you "own" the domain only as long as you keep paying the yearly fee for it. In this sense, the "ownership" of the name is not like the ownership of a physical object (eg, a car) that you buy, where once you pay for it you own it permanently. Instead, it's more like a rental fee where, as long as you pay the "rent", you can continue to point that domain name to your website.

The good news is that nowadays, because of heavy competition, domain name fees are very low. At the time I write this, prices at most registrars hover around $10 to $15 per annual.