It's not currently possible to change your Depop username for the account you currently have.
An option is closing your current account and creating a new one with your desired username. Get in touch with us at firstname.lastname@example.org and we can help you do this. We will have to check that your account has no live warnings and that you're a great user, but will get things moving.
We’re unable to provide a timeline for when this process will change, but we are working hard on creating a process that will allow username changes!