Would I have to change it through the government first? And through every other service that requires my signature? Would it cost significant amounts of money?
There is no central government signature database. (at least not in the US, and at least not yet)
For debit and credit card transactions, the merchant may check the signature on your reciept against the signature on back of the card. This is intended to verify that you didn't steal the card.
So, if you want to change the signature on the back of the card, all you need to do is get a new card and re-sign it. Your card has an expiration date. When that happens, you will get a new card to re-sign. If your card expires soon, you can just wait.
If you are impatient, you can call your bank and ask for a new card. If they give you a lot of grief about issuing a new card (it is an unusual request), you can tell them you lost your card and need a new one. In that case they will typically disable the old card and issue a new one with a new account number.
Note that if you want to change how you sign your name, there are some other places you should also update:
- All of your other debit and credit cards
- Your bank should have a "signature card" on file, which they use periodically to check the signature of your checks and endorsed deposits. You should have filled out a signature card when you opened your account. I believe most banks will let you fill out a new signature card, although you will probably have to show multiple forms of ID. (Had to do this after my wife changed her name when we got married.) Worst case, you can close your account and move to a new bank.
- The signature on your driver's license. When signing a legal document, someone may ask to see your driver's license to check it against the document. If you start signing your name differently, this may be an issue. So, you may need a new driver's license issued. Call your local DMV.
Also, keep in mind that people's signatures naturally drift over time. This fact is generally understood and accepted by people who check signatures.
This discussion over at Google Answers suggests that the only time it matters is if your signature is challenged -- that is, someone has reason to doubt it's you authorizing your signature. (Assuming US here.)
But if you wanted to get another debit card and sign it differently, and start signing things that way from then on, you might never get challenged about it.