Using my own user table

$wpdb is a global variable for the database class. In it $wpdb->users points to the name of the users table. As long as it’s the same database, you can use this to change the name of the table but it might create errors if the schema doesn’t match.

Another way is to extend the wpdb class, modify it according to your needs, then replace the global $wpdb variable with an instance of your extended class.

Other way is to go through the core & hook into every user-related function in there.

I think it’s best to let wordpress work on it’s own