Windows 8 Store
If you want to turn off the notification you get every time you install a new app, it’s easy to do so. When you install an app from the Windows Store, the Store will send a push notification on the upper right corner with the message “[name of app] has been installed.” You can click the notification to launch your new app. If you do not want to see that notification but don’t want to globally turn off notifications for all apps, you can do so from the Windows Store Settings charm.

To turn off Windows Store notifications without affecting notifications from any other app, open the Windows Store. Then, choose the “Settings” charm when on the Windows Store. From the Settings charm, click “Permissions”. Finally, under the “Notifications” section, where it says “Allow this app to show notifications”, slide the switch to “Off”. You can switch it back to “On” if you want to re-enable notifications.

Windows Store Settings

Windows Store Permissions

Hope this helps!