Ah my misunderstanding didn't read enough.
Thats a bit harder, I think what I'd do then is make an array of the alphabet to loop through and build my query with.
$alpha = array (
0 => "a",
1 => "b",
2 => "c",
etc.
Find the letter the person chose, say they chose K, then loop through the array STARTING at letter K ( use array_search() to locate it ) to make a query like this:
SELECT * FROM talbe WHERE name LIKE 'k%' OR name LIKE 'l%' OR name LIKE 'm%' OR name LIKE '%n' OR ... ORDER BY name