You can create a personal Skype Bot to get notifications from TeamCity to Skype using service AlertMePro. Register your application to get Skype Bot Id and Skype Bot Password.
1. Register or sign in to deverloper’s portal https://apps.dev.microsoft.com.
2. Press the button Add an app and enter name of your new personal Skype Bot
3. Enter name field in the next Registration page and press the button Generate New Password. Save Application Id and Generated Password any you want. Then press the button Save on this page.
4. Open Microsoft Bot Framework and sign on the page in using your Microsoft account.
Lets allow your bot send messages to group chats.
6. Press link Edit like in screenshot.
7. Then configure settings like on screenshot.
8. Add your Personal Skype Bot to your Account List.
9. Now you can start using your Skype Bot in TeamCity AlertMe Notification Plugin.