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 account 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