Super simple MEL script to do just that:

// Reorder Selected Nodes in Outliner
{
    string $sel[] = `ls -sl`;
    //print $sel;
    
    string $resorted[] = sort($sel);
    //print $resorted;
    
    for ($each in $resorted)
    {
        reorder -back $each;
    }
}

Works with multilevel hierarchy selection as well.
This is using the simple sort command, so it’s not a natural sorting method ( name1, name12, name2 will be the order).

Cheers, D