Go into the options menu and enter one of the following names as a player name. Select "Submit", and you will hear the foghorn sound if you entered the code correctly. Go into the hat menu and the corresponding hat will be unlocked:
 
Hat Name
2 (Tom Fulp) TomFulp
4 (Blonde hair) Cletus
5 (Red hair) April
7 (Jheri curl) Superfly
8 (Pirate bandana) Goodman
11 (Top hat) Grrl
12 (Diamond tiara) Abe
13 (Daisy headdress) Princess or Betty
14 (Dick Tracy hat) Dandy