You can change the name that displays with your email address, but not the email address itself. For example, changing your username/email address from email@example.com to firstname.lastname@example.org is highly not possible.
Changing your Gmail username/email address
1. You will need to create a second Gmail account > choose your desired username
2. Once that new account is created with the desired username, you can set up forwarding from the old Gmail to the new Gmail and check all of your messages in one place.
Changing the name displayed with your email address
For example, changing your name from Bob <email@example.com> to Sally <firstname.lastname@example.org>
1. Click the gear in the top right of your Gmail page.
2. Select Settings.
3. Click the Accounts tab.
4. In the “Send mail as:” section, click edit info next to the address.
5. In the “Name:” section, specify what you’d like your name to be and click Save changes.