No. You can not change your username. If you absolutely have to use a different username you'll have to register a new account. NOTE: You will not be able to use the same email address as in your first account (so change that one to and address you don't use). You will not be able to carry over any history, like forum posts and status, to the new username.
It is Dropzone.com policy not to allow multiple accounts per person, so your initial account will be disabled. Any abuse of the site through the use of multiple accounts will lead to all usernames associated with a user being disabled.
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