OLD PHONE NUMBERS SHOW WHEN USING 'MESSAGES' ON MAC ONLY.

I had this exact same issue and finally figured it out. The contact you are seeing is orphaned. You must reconnect to it and then delete.

1. Open Messages and type in the old name.
2. Select the old name that shows for a new conversation.
3. Click the arrow in the "To:" box at top of window and select, "Add to contacts".
4. Delete the conversation.
5. Open your Contacts.app and search on the old name or number.
6. Delete the empty contact.