Hi mmsyr,
Let's refresh the Message app in hopes of getting those contact photos to show. Closing the app and opening it again will accomplish this:
Phone X and later
1. From the Home Screen, swipe up from the bottom of the screen and pause in the middle of the screen.
2. Swipe right or left to find the app that you want to close.
3. Swipe up on the app's preview to close the app.
You can find these steps along with other information that may be helpful, here: Close an app on your iPhone or iPod touch - Apple Support
If you have followed the steps correctly and you still have the issue, let us know if you get any specific alerts or error messages when trying, as those may help us determine what might be causing the issue.
We also recommend restarting your device and keeping it updated as those steps assure you have cleared out any minor software issues and are running the most current version.
Restart your iPhone - Apple Support
Update your iPhone or iPad - Apple Support
If you still have questions, reach out to Apple Support directly, as this may require closer guidance: Get Support
Cheers!