It is possible to purchase a name change in Marvel Heroes, but there is currently not an automated system that handles it. However, it's really fast and easy, and currently costs 1,000G (which is around $10).
Firstly you need to log in to your profile at Marvelheroes.com and click on "Support". This will let you create a ticket, and make sure to change the ticket type to "Paid Name Change Request". Now simply type in your new desired username in the ticket field, and it will be changed soon. It might take a little while, but it only took like 10 minutes both of the times I did it personally.