Finding out your Skype ID is easy and you have 2 options to do so:
1. Go to the main page where you can register a new SkyPrivate account: https://accounts.skyprivate.com/users/register/ and click on "Don't know your Skype ID? Find it here."
Fill in your e-mail address you used to create your Skype account and click on "Submit".
After doing this, your Skype ID will be autofilled in the first field of the form.
2. Log into Skype for web here: https://web.skype.com/ , then click on your name in the top left corner of the screen. Your Skype ID will appear under your name. (as a note, "live:" is part of your Skype ID if you've created your Skype account using an e-mail address or phone number)
You will be logged into Skype for web (make sure that you don't try to use the SkyPrivate plugin on Skype web since it won't work).