In the early days of Newgrounds it was easy for a User to change their Username, and commonplace. Now it is difficult for the User, because it is difficult for Newgrounds administration to do. As explained by Malachy:
" For all intents and purposes your username is permanent. Previously your account was tied to a unique user ID and your profile was a pop up box with some information. That changed in 2007 when the site was redesigned and each profile was given it's own page and url based on the user name. Your username is part of a permanent page of the site that has a specific URL (username.newgrounds.com) To change your username, the staff need to change the URL that leads to your user page."
Possible, though unlikely Edit
A User should PM Wade with a good reason why and he will consider it. Due to the great pile of PM's Wade receives, a user may not even get a reply, if nothing is heard in a month or so, it is unlikely to happen. The WI/HT team presume that Wade is more likely to do so for someone with a significant User account, with perhaps a number of submissions etc. and generally advise users with a small recent account just to start again with a new account.
If you are stuck with the name Edit
"If you want a desired username you are welcome to make a new account with the name you want. If you want to use the same email you used for your current account, you will need to change the email for your current account so that you can create a new account using it (otherwise you get an error message saying the email is already in use for an account)."
If a user wishes to keep the submissions from his older account on the new one, it is possible to co-author the new account on to the old movies.