No; once an edX username has been created at registration, it cannot be changed.
Workaround: Create a new edX account
You can create a new account using an unused email address to have a different username. Please do not delete your account if you want to create a new account using the same email address. Once an account has been deleted, its email address cannot be used again to create a new account.
Create a new edX account using the same email address
If you would like to use the same email address on a new account, you will first need change your email address on the existing account to any unused email address.
You can edit your email address from your Account Settings. Under Account Information, click on "Edit" next to "Email address (Sign in)." Type in your new email address, and click "Save." There will be a message "We've sent a confirmation message to 'email address'." Click the link in the message to activate your updated email address.
Once updated, your original email address will be available to use on the new account.
Note: Progress will not be transferred
Please note that since we're not able to merge accounts, if you decide to create a new account so you can use a different username, any progress you made on the original account would not be available on the new account.