2 Answers

If by EDIT you mean CHANGE your email address....see below
You can't change your name but you can add another to your present account OR make a new one....see below
To clarify what is below...when you add another name to the present account you will not lose anything...IE: contacts...address list. etc...You will have to send an email to all your friends advising them of the new email address...if someone makes a mistake and sends it to the email address you don't like anymore it will go to the same inbox so you don't lose any messages.
Click the link below to get an extra email address for your existing account. It´s absolutely free. Use it just as you would for your primary address (which of course you can still use). To make things handy, you can send and receive email from either address from the same inbox. http://edit.yahoo..com/config/list_alias…
To notify your contacts of the email change click on OPTION...MAIL OPTIONS...go to the left side and click on ACCOUNTS..then click on ADD OR EDIT...go back and click on MAIL again...Under MANAGEMENT scroll down and click on ANNOUNCE EMAIL ADDRESS...once you are done with what you want the notice to say AND after adding your contactlist in the header click on PREVIEW AND SEND....when the new screen comes up and everything is as you want it...go below and send it....

Should you want to make your secondary email address as your primary you can click on OPTIONS...MAIL OPTIONS...go to the left side of the screen and click on ACCOUNT INFORMATION...submit your password again and once in to your account you will see EMAIL INFORMATION..Click on designate which one you want as your primary Then click on SAVE.

Source :Yahoo answers

If you are asking about your own e-mail address, it can not be changed or edited. You would have to create a new e-mail account in order to change your e-mail address name and the way it appears.