You can change your username by going to Username > Your Profile and finding the Username field. Once you’ve updated your name, scroll to the bottom of the page and click Save Profile.
Keep in mind that your username appears in the URL of your account’s subscribe form and archives page, and updating your account’s username will also change the URL for those public pages.
For example, if your current username is set as jessepinkman, your subscribe form will live at http://www.tinyletter.com/jessepinkman. If you update your username to walterwhite, then your subscribe form will live at http://www.tinyletter.com/walterwhite.