As per Facebook, the new page might not be able to create a username right away. A page must fulfill two requirements to allow users to generate usernames. It has to have a minimum of 25 likes on the page and a minimum of one post. After you complete the prerequisites, try to create a username for your page. The error This page isn't eligible to have username will most likely appear if the conditions aren't met, The 'this Page isn't eligible for a username' problem has a solution by making the appropriate changes and assigning another account as Admin.