Apple has changed up quite a few things regarding notifications in iOS 11. They've added optional persistent notifications, made it possible to disable notification previews for all apps, and changed "Notification Center" to "Cover Sheet." In the process, they've also included another handy feature — the ability to hide certain app notifications from appearing in your Recent Notifications list.
Firstly, if you didn't catch that, what was called "Notifications View" since iOS 7 is now called "Recent Notifications" in iOS 11. Just wanted to clear that up if there was any confusion. These are the notifications that can be viewed when you pull down from the top (or swipe up on the lock screen) to view your Cover Sheet, which shows new and recent notifications from apps.
If you'd like to continue seeing new notifications for apps as they come in, but don't want them clogging up your Recent Notifications section in the Cover Sheet, you can prevent them from being listed in your history here. Just tap on "Notifications" from Settings, then select the app you want to hide. In the app's notification settings, toggle off the new "Show in History" option.
Now, whenever you pull down (or swipe up) to see your Recent Notifications on the Cover Sheet, you won't see that app anymore in the history. Do this for each app that you'd like, and your Recent Notifications history will be cleaner than it ever was before. Just note that new notifications from the app will still appear up top on the Cover Sheet, they just won't persist into the history section later.
In the screenshot above on the left, you can see that the "Yahtzee" app is still visible. After toggling "Show in History" off for it, it disappears from the "Earlier Today," "Yesterday," and so on sections of the Recent Notifications (middle and right). However, new notifications are still present (middle), but won't stick around.