Your radio profile is created when you create your radio. You can always update your radio information, here how.
How to edit your radio profile
Select the radio on which you want to edit the profile.
Go to Settings > Profile.
The Public URL is unique to your radio and is used to deliver assets like the player to your listeners. When you change your URL, all your current shared links will stop working. You will need to update all your integrated tools and links with the new one.