The term for the authority that regulates and governs internet domain names is the Internet Corporation for Assigned Names and Numbers (ICANN). ICANN is responsible for overseeing the domain name system and ensuring that each domain name is unique and functional. They also manage the allocation of top-level domains (TLDs) and IP addresses, which are crucial for maintaining order on the internet. By setting policies and guidelines, ICANN plays a vital role in the stability and functionality of the global internet infrastructure.