No problem, you can change your public username by logging in to your account and going to your profile page.
Click on the dropdown menu at the top right of the page next to your profile icon and click on 'My profile'. Then click on 'Edit profile'.
Scroll down the page and you can then enter a new public profile name. Please remember to save the changes!
If you pledge on a project, this is the name that will show publicly on the 'Supporters' tab on the project page, unless you tick to pledge anonymously.