Yes, you can control which events you receive alerts for. Not all notification settings are available to change on all platforms. You’ll need to sign in to Skype on Windows desktop or Mac to change some of these but once changed, they will sync and persist across any other device.
on Mac: Go to Skype > Preferences > Notifications, then check or uncheck each notification type to turn it on or off.
on Windows desktop: Select Tools > Options > Notifications then check or uncheck each notification type to turn it on or off.