Gmail – Creating New Gmail Account

You can logout of your Gmail account, and then sign up for a new account. Once you've created an account, go back to your original account and forward everything to the new account.

You can not change your Gmail address. You will have to create a new email address, copy all your account data (old mails, contacts, labels, etc.) to your new account and forward any incoming mail to your old account into your new account.

For migration you could use: Gmail Backup and follow the FAQ on migration.

Additionally you should check out this Google Help article for migration of services associated with your account you might not have thought about.