TO CHANGE THE DISPLAY NAME IN GMAIL
After logging into Google Mail, click the Settings link. This will open all of the settings options for the Mail portion of Google Apps.
Click on the Accounts link to show the following page. In the section titled Send Mail As choose the edit info link at the right-hand side of that section.
Choose the radio button next to the text box under your name and type in your preferred Display Name and click Save Changes.
This will take you back to the Accounts page of the Settings section and you will see how your name will appear in the From field of emails sent from your account.