Log into your Gmail account and click Settings (top right) -> Accounts -> Send Mail
As: ... Add another email address...
Add firstname.lastname@example.org as an email address, you will receive a verification email from Google that goes something like this:
You have requested to add email@example.com to your Gmail account.
Confirmation code: 1234567
Before you can send mail from firstname.lastname@example.org using your Gmail
account (email@example.com), please click the link below to confirm your
If you click the link and it appears to be broken, please copy and paste it
into a new browser window. If you aren't able to access the link, please log in
to your Gmail account, and click 'Settings' at the top of any page.
Open the 'Accounts' tab, and locate the email address you'd like to add in the
'Send mail as:' section. Then, click 'Verify,' and enter your confirmation
Thanks for using Gmail!
The Gmail Team
Once you have verified your address, you can then set it as your default address by clicking the "make default" link next to the address in the Settings --> Accounts tab. Then your Gmail emails will come from your-domain-name.com.