Unfortunately, the only way to do this is by creating a new account with a new username.
Reddit does not provide room to change your username, but, you can look at the opportunity as one to reinvent your account.
How To Change Your Reddit Username
Open reddit.com in your preferred browser and sign out of your existing account if you were already signed in.
Do this by clicking on the arrow seated next to your name on the top right corner. Click on Log out at the bottom of the drop down list that is displayed.
Again, at the top right corner, click on Sign up. Now input your email address and click Next.
Input your new username, enter a new password and then click Sign up to set up the new account with a new username.
