Hello MissGreenBeanz,
Welcome to Apple Support Communities!
We want to help get your photo showing like you expect on the shared list.
Let's start by making sure you assigned the reminder using these steps:
"Assign a reminder in a shared list
- Tap a reminder.
- Tap the Assignment button
in the quick toolbar. - Choose the person you want to assign the reminder to.
- Tap Done.
Need to reassign a reminder or remove an assignment? Tap the assignee next to the reminder, then tap Reassign or Remove Assignment."
Detailed here: Share and assign reminders on your iPhone, iPad, or iPod touch - Apple Support
Make sure your photo is added correctly to your contact card also:
"Edit My Card
Tap My Card at the top of your contacts list, then tap Edit."
If the issue continues on your Mac, try restarting it as well.
We hope this helps to quickly resolve the issue so your photo shows as expected.
Cheers!