Hey Tom,
Thank you for using the Apple Support Communities!
That's called the Share Sheet in iOS. Typically, on-device processing helps identify which contacts and apps are displayed based on how you use your device and apps. If it's not showing anything at all, let's see if we can determine what's affecting it.
On your device, navigate to Settings > Siri & Search. Under Suggestions from Apple, do you have 'Show When Sharing' turned on? Then, on that same page if you scroll down a bit you'll see a list of your apps. Open the applications individually (that you wish to be able to show up) and make sure 'Suggest App' is turned on too.
Let us know if that has an impact on what you're seeing. If you did need to turn those settings on, be sure to use your device a few days to allow the on-device learning to kick in.
Best regards.