Option 1: Create a seperate email account (Google will charge you for an extra user, usually around $5/month). Click "Users" and add a completely new user this way.
Option 2: Setup a free diversion from one email address to another at your domain.This is a called an email "Alias". For example, if your main email address is firstname.lastname@example.org you might want to setup an alias so email@example.com also arrives here. Click on "Users" then click on the specific user you want to add an alias to . Then click "Account". Then scroll down to Alias and click "Add Alias".
Don't forget to test your new email address, and remember Google wont let email yourself or an alias of yourself from the same Gmail account. So get someone else to email you or use another email account for testing.