If you want to use alternative email address instead of your original gmail address, you need to provide details for an SMTP server which will be used to send the mail.
The first action you should do is → Settings → Accounts → Add another email address like below
Then you will see popup window like below
When you click "Next Step", you will see following:
If you have smtp server available, you can use it. Otherwise, please follow below
smtp.gmail.com
@
gmail.comote that you should put your user account including domain name if you use personal domain name like foo.com