The organization that coordinates the global Domain Name System is ICANN, the Internet Corporation for Assigned Names and Numbers. It helps coordinate the DNS root, top-level domain registries, and the allocation systems that allow domain names and numerical Internet identifiers to work globally.
ICANN was established in 1998 as a nonprofit, multistakeholder organization. Its coordination role helps ensure that a domain such as example.com refers consistently to the same DNS hierarchy regardless of where a user connects. ICANN does not operate every DNS server or register every domain directly; registries and registrars perform much of that operational work.
The IANA functions are closely related. IANA maintains important Internet number and DNS root-zone registries, and those functions are performed within the ICANN ecosystem. This is why IANA and ICANN are sometimes confused, although they are not interchangeable answers to every DNS question.
The IETF develops Internet protocol standards, W3C develops Web standards, and ISOC supports Internet development and policy. None of those organizations is the canonical answer to this question.