When new user register then add new user role

The user_register hook passes the parameter $user_id to your function. Get the login name after instantiating a user object with get_userdata( $user_id ).

Update the assigned user role with wp_update_user. Alternatively, you can use add_role to assign the new role in addition to the currently assigned role instead of removing the currently defined role with wp_update_user.

add_action( 'user_register', 'abc_assign_role' );

function abc_assign_role( $user_id ) {
    // Instantiate user object.
    $userobj = get_userdata( $user_id );
    // Define new role using the login name of this user object.
    $new_role = $userobj->user_login;

    // Create the role.
    add_role(
        $new_role,
            __( $new_role ),
            array(
            'read'         => true,
            'edit_posts'   => true,
            'delete_posts' => false,
            )
    );

    // Assign a new role to this user, replacing the currently assigned role.
    wp_update_user( array( 'ID' => $user_id, 'role' => $new_role ) );
    // Assign additional role to the user, leaving the default role that is currently assigned to the user.
    // $userobj->add_role( $new_role );
}