Finding out your Skype ID is easy and you have 2 options to do so:
1. You go to the main page where you can register a new account: https://accounts.skyprivate.com/users/register/ and click on "Don't know your Skype ID? Find it here."
You fill in your e-mail address you used to create your Skype ID and then click on submit.
After doing this, your Skype ID will be auto filled in the first field of the form.
2. You just have to log into Skype for web here: https://web.skype.com/
Enter your credentials