Currently, q2a admin can specify whether users can change their usernames or not. However, admin can not specify howmany times a user can change the username.
Gateoverflow team is developed a plugin (it consists few more small features) for limiting the number of times a user can change their username. Admin can specify the count through the admin panel.
Interested users can check and download the plugin from github:
https://github.com/GATEOverflow/q2a-miscellaneous-settings
