You can delete player profiles when you're logged in to HockeyShare by going to the 10k Pucks link and selecting the "Players" option. Simply click the "Edit Profile" button for the profile you wish to delete. In the lower-right corner of the Edit Profile page you will see a red "Delete" button.
Please note that once a player profile has been deleted, so has all of the shots recorded for that profile. This data cannot be recovered.