After you've made a PlayStation Network account on your PS3, you can't completely delete it from Sony's servers. However, you can still remove the account from your console and refrain from logging in. Alternatively, to guarantee you'll never be able to log in again, you can unlink your account from your console and request that Sony suspend it.
Removing the Account
Removing an online account from your PlayStation 3 console takes just a moment. First, highlight your profile, then press the "Triangle" button and select "Delete." If you don't feel like contacting Sony to suspend your account, this is the only action you'll need to take.
Suspend Your Account
If you're planning to suspend your account, you have to deactivate the console first. This will let you use the console again with another PSN account in the future. Under "PlayStation Network" on the XMB menu, select "Account Management." Select "System Activation," followed by "PS3 System." Pick either "Game" or "Video," followed by "Deactivate System" to fully remove it from your account. From there, you can contact Sony to request a ban on your account.
If you close your PSN account, you won't be able to access anything you purchased on the account, you'll lose any funds remaining in your wallet, and anyone who has a sub-account under your master account will also lose access to the PlayStation Network.