Please add the code given below to stop users to change their name in your wp-content/plugins/wplms-customizer/wplms-customizer.php.
function disable_name_change( $data ) {
if ( 1 == $data->field_id )
$data->field_id = false;
return $data;
}
add_action( 'xprofile_data_before_save', 'disable_name_change' );