You have both a Username (used to log in) and a Display Name (displayed on recording pages, etc). By default, your Display name will be the same as the Username that you use to log in.
Changing your Display Name
You can customize your Display Name and your Account Email under account settings, but you cannot currently change your Username. I've added your vote to a feature request to allow users to update their own username in their Zencastr account settings. It's definitely something others have asked about.
Changing your Username
In the meantime, Support can change your login name for you. If you'd like us to do this, please write in from your account email and confirm your current Username and let us know what you'd like it changed to. We suggest providing us with a few options (listed in order of preference) just in case your top choice isn't available.