Transform user name before displaying

Hard to say without seeing any code as to how you are building it out but one suggestion would be to update the field on submit prior to running your register_new_user function.

PHP strtolower() Function can be used when passing the data to your custom field

Javascript/jQuery you can use .toLowerCase() on the field

Hata!: SQLSTATE[HY000] [1045] Access denied for user 'divattrend_liink'@'localhost' (using password: YES)