Currently, if you would like to change your account's username which is part of your web address/URL, you would have to create a new account with that new username, upload your publications to this new account, and close the old account.
At this time, it's not possible for us to move documents from one account to another, so you would have to re-upload your documents to the new account for them to appear in search results under the new account. Any statistics that were associated with a publication on the old account will not be transferred to the new account when you re-upload them.
Please make sure to use the email sign up option, not the Facebook or Google+ options, as those will auto-populate the username section, and you currently won't be able to change your account name and web address after that. (Please see photos below.)