Go to the Settings page:
Then go to the ACCOUNT tab and click on the "Delete your account" button:
What happens if you delete your account?
Once your account is deleted, it CANNOT be recovered. You won't be able to log in with this account any more.
Anything you created on Listen Notes will be gone as well, including Listen Later playlists, Listen Clips, Listen Alerts...
If you are an API user, your API tokens will become invalid.
If you just want to prevent others from finding you on Listen Notes, you can change your privacy settings.