switch combined with if statement

You do not need to use pass the $value in a switch statement, Just pass there $user->roles[0] instead of $value and after that your condition.

Add below code and let me know your answer towards it.

add_action( 'um_members_just_after_name', 'my_members_after_user_name', 10, 1 );
function my_members_after_user_name( $user_id ) {

    $user = new WP_User( $user_id );
    /*
    if( $user->roles[0] == 'um_musiker' ) {
        // update_user_meta( $user_id, 'um_reihung', '40' );
        echo '<i class="um-verified um-icon-checkmark-circled um-tip-s" title="Kein Status"></i>';  
    }
    */


        switch ( $user->roles[0] ) {
        case "um_musiker":
            echo '<i class="um-verified um-icon-checkmark-circled um-tip-s" title="Kein Status"></i>';
            break;
        case "um_musiker_bronze":
            echo '<i class="um-verified um-icon-checkmark-circled um-tip-s" title="Bronze Status"></i>';
            break;
        case "um_musiker_silber":
            echo '<i class="um-verified um-icon-checkmark-circled um-tip-s" title="Silber Status"></i>';
            break;
        }

}