display_name, and any active member can change it.
Rename with PUT /v1/chats/{chatId} (reference); the SDK method is relay.chats.update. display_name is a string of 1 to 255 characters, and sending only the name leaves the photo unchanged. Relay answers 202, records a group-history event, and emits chat.group_name_updated.
Read the chat back to see the new name. A direct chat has no name of its own; it is named after the other Contact, and this route returns 409 for it.
Rename the group
Send the new name:display_name before you retry an uncertain update rather than sending the same name twice.