There are a few large and vary many small companies that will register an unused name on your behalf for a yearly fee.
Expect to pay about ten dollars a year. Domains use to cost a lot more than that. If you pay a lot less, expect to be pitched a lot of add-on features that you probably don't want.
ICANN is the organization that ensures that this process proceeds orderly. They publish a list of accredited registrars .
Many registrars have exotic features that support people who hold hundreds of names like land speculators. These make getting your first name confusing. Be patient. Explore.
For what it's worth, I've registered wiki.org at name.com .