Just the thought of possibly contradicting Weedpacket makes me a bit quesy but here goes.
Your original code will work fine assuming you have the input statements surrounded by form tags and a submit button. Notice however that
$LName[key] should be $LName[$key]
And if register globals is off then you need to pull out the name arrays before your while loop.
$FName = $POST['FName'];
$LName = $POST['LName'];
$Players = $_POST['Player'];
foreach ($Players as ...
Using just the [] in your input elements without filling in an index is fine.You will have trouble with check boxes since only the checked boxes will get posted back. Your hidden field's value should probably be the person's database id number so you know exactly what persone is being worked on.