Final answer:
The core responsibility of ICANN in Internet governance is managing domain names.
Step-by-step explanation:
The core responsibility of the Internet Corporation for Assigned Names and Numbers (ICANN) in Internet governance is managing domain names. ICANN is responsible for coordinating and managing the domain name system (DNS), which includes the distribution and management of domain names and their associated IP addresses. ICANN ensures that domain names are unique and properly resolved to the correct IP addresses, allowing users to access websites through domain names instead of IP addresses.