After signed up with our web hosting you will be able to use professional looking own domain email email@example.com. However your existing customer might still recognize your free email.
Checking several inbox will be time consuming. To overcome this, we can make use of email forwarding. Email forwarding is an email feature to automatically forwarding email received on one email to another email. So you just need to check one email account.
Usually mail provider required you to click verify link on email to proof that you are the owner of the destination email that request email forwarding. This is to prevent abuse user to forward unwanted emails to you.