Contact is displayed as number, and is sent to myself and the contact

Exact same problem (I am on iOS 18.0.1 but my contact was still on iOS 17 when the problem emerged). Opening the Messages app shows everything normal, with it correctly associating the number with the contact, except like OP I've also lost access to a couple years of the chat history on my phone. The problem with the notification likewise occurs only on my iPhone, not on my iPad or laptop or Apple Watch (all are similarly running the latest OS). On all those other devices, the notification looks completely normal and chat history looks normal. One curiosity: on my iPhone, for a while the notification changed to display "Maybe: (contact name) to you & (contact name)", but in my attempts to delete and restore the contact and try other troubleshooting, it has now gone back to showing the number as shown in OP's image here. Maybe Siri will eventually start suggesting "Maybe: contact name" again, instead of the number? In any case there's no way to confirm the "Maybe" and force it to use the name on the contact card that it's correctly guessing.

One thing I've determined: the name of the contact after "To you &" comes from the Apple ID email address belonging to the contact (which is used somewhere deep in the chat history as the recipient or sender of an iMessage). So the behavior seems to be a result of iMessage breaking the association to the contact card of only the phone number, which it then sees as sending a message to a thread that includes that same contact's iMessage email address as one of the participants. The problem doesn't occur with SMS texts, which trigger a normal notification when sent from the contact. (Side note: a related problem sometimes occurs with the new RCS texts, sent after my contact upgraded to iOS 18 as part of our attempts to fix, but in those RCS text cases, it's my laptop app that experiences split threads and weird notifications, while the iPhone behaves normally!)

To try to fix it I even completely deleted the contact, and created a brand new contact directly from a new iMessage received from that number, but after doing so it has just resumed the behavior shown by OP. I've also tried a long list of other tactics such as having the contact sign out of iMessage/FaceTime and back in, doing the same thing myself, and many other things, even going so far as to redownload the eSIM, but it has not helped. The problem first emerged about a day after we ported the number from a SIM with one carrier to an eSIM with a different carrier, but that may have been a coincidence since the phenomenon seems to be occurring with iOS 18 users who have not recently changed anything about their phone service.

This exact same thing is happening to me. Whenever I text my daughters Apple Watch, it says "To you & ...@icloud.com" but is not happening when my husband texts her.