I have been actively trying to troubleshoot this and trying different things.

I removed my SIM card from my iPhone on iOS 18 and put it into a second phone(iOS 15). They turned their iMessage send and receive to only their number and turned SMS forwarding off from all their devices. I didn't sign into my Apple ID and it showed as their number and the expected behavior. I signed into my Apple ID and it showed as the expected behavior. I do not have iMessage enabled in iCloud. And iMessage was disabled on my primary phone. I now have them change their iMessage settings to what it was before("send and receive from" back to their number and emails, and the "create new convo" to their email.) This still has the fixed and expected behavior of only showing it coming from their number in the notifications. I am using the phone number for iMessage, not my Apple ID.

Now I have working messages on a second phone. Now I just need to get it to work on my primary phone.

I then use my Apple ID for iMessage and that still works.

So now I’m really thinking the problem might just be an overlooked iOS 18 bug? But what would make it only with their contact? I'll try to factory reset my iOS 18 phone and see if that changes anything, and if it does then I suspect that it's the thread that is corrupted somehow.