Other domains have a single registrar. For example, the .edu registrar is a professional society called Educause. Eligible educational institutions can register an unused domain name for $40 per year.
Some country code top level domains have a single registrar, others many.
Once you or your organization owns a domain, you can assign (fully qualified) names within it. For example, if I wanted a new server called lp.csudh.edu, I would request it from our campus DNS administrator. He or she would then enter it into the table maintained on our campus DNS server, where it could be discovered by others. As you see, the system is decentralized.