Update My Gmail to Reflect a Name Change

Open your gmail inbox in a browser (like Chrome) and click on the gear icon in the upper right corner to locate the settings menu.
Choose the accounts section, and in the “Send Mail As” section, click “Add another email address you own”.
Enter your new name and new address (if one has been provisioned for you) in the respective boxes, and then uncheck the box next to “Treat as an Alias” before clicking “Next Step”.
You should now be back to the “Accounts” window (like step 2 above) but you will see the account you just added in the list of “Send mail as” accounts. To the right of that new address, click on the “Make Default” link.
As long as you see “default” in grey text next to the new name and address, you are all set. From now on when you send someone an email, it will come from the new email address with the new name attached.