I have seen advertisements for domain-name registration by companies not in the accredited registrar directory. Are these legitimate?

Only registrars accredited by the Internet Corporation for Assigned Names and Numbers (ICANN) are authorized to register .aero, .biz, .com, .coop, .info, .museum, .name, .net, .org, or .pro names. Some of these accredited registrars offer their services through resellers, which may provide assistance in completing the registration process. Your registration contract, however, will be with the accredited registrar and that registrar will maintain your contact information.