To use Skype for modern Windows with multiple accounts, you need to have a Microsoft account linked to each Skype account you want to use. If you haven't already linked your Skype account to a Microsoft account, you can learn how here.You can sign in to Skype for modern Windows with different Skype accounts by creating separate Windows 8 user accounts with seperate Microsoft accounts.
However, if you don't want to create separate user accounts (or don't want to link existing Skype accounts and Microsoft accounts), you can also use the Desktop version of Skype on your Windows 8 and above device. Learn more.
When you've created a new Microsoft account or linked a Skype account to a Microsoft account, you can then set up differen user accounts on Windows 8 and above.
This option will give you separate Windows 8 user accounts. Each of these user accounts will have its own Microsoft account you use to sign in, just as if the accounts were on seperate computers. This option is perfect if different people are using the same computer, or for using separate Skype accounts on Windows 8 or 8.1 devices.
To sign in to Skype for modern Windows with different accounts:
Your apps, settings, and documents are linked to your user account. If you switch to another account, you won't have access to them until you switch back (or unless you duplicate these on your new user account).