Your profile picture is used everywhere you are logged in with your Microsoft Account, but it doesn’t always look good in every app. Here is why and how to fix it.
Apparently there is no way to add or link an account to Skype while the application is running. I always ‘Auto Sign-on’ with Skype. So, I had to log off Skype, then choose ‘Login with Microsoft Account’ option, then it will present you with the option to merge accounts. Then, you will see this under … “How to add your Microsoft (Windows Live) Account to Skype”