not sure I am with you but...
if you want a unique name for every checkbox just add a variable into the loop.
ie:
<?
$x=0;
while($thisrow=$mysql_fetch_row($result)){?>
<input type="checkbox" name="box<? echo $x"?>"><br>
<? $x++; }?>
then you have box0,box1,box2 etc etc
hope that was what you meant!
Simon.