It's possible to change push notification message before display on device from iOS side?

There are various possibilities for preprocessing and modify the payload of a notification on iOS.

Before iOS 10

You could be sending Silent Notifications, what will not be not shown to the user. Will wake our application when it is terminated or in background, and you will be able to do preprocessing on the notification content. See more info here, how to set it up. However, this notification type is not 100% reliable, and should not be abused, e.g. used for all notifications to be delivered, because Apple could stop the notifications to be sent after a number of messages.

The other option is, if your application supports VoIP. This way your app will pretty much always listen to push notifications, and you will be always available to preprocess the notifications, before you would be displaying them. However, if your app does not have real VoIP capabilities, e.g. phone calls, your app will be rejected by Apple on the review. Here is a great tutorial, how to set it up.

From iOS 10

With the introduction of iOS 10, we are finally able to do preprocessing on our notifications, even, when the app is in background or terminated. No VoIP capabilities or special type of notifications needed to be sent. Here is a great tutorial, how to set it up.