Currently you cannot change the username associated with your Snapchat account.But you can, delete your old account and then create a new account with a different username. Alternatively, you can change your display name, which is the name your friends will see when you send a Snap or a chat. To change your display name-
• Go to your main screen and open snapchat app
• Enter your username and password.
• Swipe down from anywhere on your screen to open your Snapchat account page
• Tap the Gear shaped icon it’s in the upper-right corner of the screen and will navigate you to the Settings menu.
• Tap name, it’s at the top of the menu.
• Enter your new display name. Be appropriate to choose a name that’s recognizable to your friends.
• Hit save.
• Congrats your display name is changed.
You cannot change the name of your snap chat acount.
Currently the username on an existing Snapchat account cannot be changed. The official support document from Snapchat states: For security reasons, it is currently not possible to change the username for an existing account. If you wish, you may delete your account and create a new one.