Hello SlowLearner...,
Welcome to Apple Support Communities!
I understand upon attempting to edit the name and photo in messages you received a message saying Message Sharing name and photo not available. iCloud & iMessage accounts are different or are not signed in. I am happy to help you.
Have you restarted your phone since this happened?
Restart your iPhone
Maker sure that your iOS on your phone is up to date.
Update your iPhone, iPad, or iPod touch
Check and see if you're using multiple phone numbers for your Apple ID.
Settings > Messages > Send & Receive.
If you do have multiple numbers remove the phone number that is not being used.
Add or remove your phone number in Messages or FaceTime
Let me know if that worked for you.
Thank you for using Apple Support Communities.
Take care!