Using the email address as the username in membership

I am developing a web site which will make use of the membership framework to validate users. It is common to set (or ask through a user interface) a user name, an email address and a password for each user, but I have thought about using the email address as the user name so the user saves from defining one piece of information. My UI would only ask for email address and password and, in code, I would set the user name equal to the email and add the record. At first, it seemed a good idea to me but I am realizing that the user might want to change his/her password and, in such a case, this implies to change the user name which is also the email address. In other words, if the user wants to change the email address, maybe I would need to setup a new user. I am writing to ask for feedback about this approach.
Respectfully, Jorge Maldonado