Typically, name changes are handled at the state or province level in North America. In other countries, they may be handled at the national level.
Google your stete/country's name change requirements. Anyone can usually have any name they want, provided it is not for fraudulent purposes. Some jurisdictions have measures in place to prevent fraudulent or criminal reasons for name changes. Where I live, for example, you need to be fingerprinted, in order to verify whether or not you have a criminal record. It doesn't mean that you can't get a name change, it is just to ensure that any record has all relevant names and aliases recorded on it. Probably not a big concern for a minor. But the point is to find out what the actual requirements are where you live.
Since you are dealing with bureaucracy, you need to do it right, or you will encounter delays. I omitted some supporting documents and had to wait an additional month while I rounded up the right documentation. In most places, there will be a fee for the name change.
In some juristictions, like where I live, the procedure is strictly bureaucratic. You fill in the forms, supply the documents, pay your fee, and you get your name change. In other jurisdictions, the process is judicial. You need to go before a judge and explain the reasons for the name change.
So there is no one answer that fits all circumstances. Most places have websites now that describe all of the necessary procedures.
