It is possible to add your custom email account “email@example.com” onto your gmail Inbox and Manage it from there. You can follow the steps given below
1) Login to your gmail account
2) Click on the Gear Icon on your top left corner.
3) Click on the setting option.
4) Click on Accounts and Import Tab.
5) Under the section “Send mail as:” click on the link “Add another email address you own”.
6) It will ask for name and email address.
Name : Any name
email address : firstname.lastname@example.org
Check the check box “Treat as alias”
7) Enter the password of the email account, select the port as 465. It will automatically enable the SSL option.
8) Once the credentials are verified, it will send the verification code to the email address you are setting up. In this case it will be “email@example.com”. Login to “firstname.lastname@example.org” to retrieve the verification code and paste it to the box.
9) Now you will see that the account has been added to your gmail account. Please choose the option “Reply from the same address the message was sent to”. Because if not selected, when you reply to the email which is received at “email@example.com”, the from address will be set as your gmail address.
Now all is set. You can manage the address “firstname.lastname@example.org” just we manage our email accounts in Mozilla Thunderbird and MS Ooutlook. Have a Great Day!!!