How do I manage notifications in the new Skype on desktop?

Yes, you can control alerts for specific conversations in Skype.

1. Select a conversation or group from your recent chat list.
2. Select the contact or group name at the top of your chat.
3. Scroll down to Chat Settings and toggle notifications off or on for that chat.
   
   Alternatively for group chats, you can enable Smart notifications, so you will only be notified when you are quoted or @mentioned.

There could be a few reasons why you might not be receiving notifications:

• Notifications will stop when you sign out of the app. Make sure you are signed in.
• Make sure your Notifications for conversations is on.
• If you are in Do Not Disturb mode, you will not receive chat notifications by default.  You can change that behavior by selecting your profile picture, then in Application Settings, under Notifications select Show chat notifications while Do Not Disturb is on.
• Verify that you haven't turned Skype notifications off from your device settings. Settings are managed differently depending on the device. If you’re not sure how to check your device settings, you may need to check the manufacturer’s website.
• Make sure you haven't turned notifications off for a specific conversation.
• Make sure you're using the latest version of Skype.

If you close the Skype app without signing out first, you might still receive notifications. If you want to stop these notifications, you can either disable them from your Settings or sign out before you close the app.