Speaking specifically about .com/org/net/info I would not use either the word 'rent' or 'own' strictly but defacto you own the domain if you continue to pay the really nominal fees every year for renewal with the registrar you choose. That is an entire topic in itself because different registrars have different policies subject to (again for those tld's) ICANN rules.
As such you 'own' the rights to the domain name (same as google, amazon, tesla etc) in the sense that you can sell those rights to someone else if you want or transfer them.
You can think of domain ownership similar to physical real estate where there are property taxes you pay. There are a limited set of circumstances where you can lose the property (don't pay property tax, eminent domain etc) but you don't think you are renting (other than if you are renting).
Now for other things you own there is no annual fee you pay.