Keep your email address, but always use a UNIQUE password for your email address and make it different from one that you use to register for web sites.
One of the problems nowadays is that when we register for web sites we often use the same email/password combination to register for the web sites that you use to logon to your email system.
So on a dodgy web site you are "giving away" your email address and password combination so anyone can steal it and log on to your email system.