Hi Sandman,
I wasn't exactly sure which user name you are referring to, however I would have to guess you are talking about your Contacts Portal User Name. If this is the case, I don't believe Customers have this option from any stock screens. However, it would be possible to customize your Contacts_Portal screen to offer them this option. I am not too sure how familiar you are with doing customizations in Method, however I can give some details if you have done some in the past. I did a quick test in my own account, I added the PortalUserName field to my Contacts_Portal_EditProfile screen, then updated a couple area's on this screen to get this value from the table and display it when the Contacts goes to edit their information. Then, I had to make sure I was storing this value back to the table when the Contact presses the save button after updating the field. I took a screenshot of this quick example:
Please let me know that this is what you are looking for, if you are comfortable with customization your screen, I can let you know which areas from the stock screen I had to edit.
-Ben