The signature should match the payee. In other words, the endorsement should appear and be spelled the same as what’s written on the check (where it says "Pay to the Order of"). When there are multiple names there, you may or may not have to get signatures from everybody.
You may also want to consider adding additional information or restricting how the check is used. If you simply sign your name, anybody can cash the check. However, adding limitations (instructing that it only be deposited to your bank account, complete with your account number) can reduce the risk of headaches and stolen money.
