Messages.app notification only shows contact number instead of contact names on macOS
I managed to fix this by going to System Preferences &gt; Language &amp; Region.  I changed the default language from English (UK) to English (Canada) and quit System Preferences.  I then changed the default back to English (UK) and then quit System Preferences again.  I then restarted macOS.
I have absolutely no idea why that works.  From the number of similar posts on the internet proposing different solutions, I suspect there are multiple possible issues leading to the same problem.  However, this it worked for me on macOS Big Sur 11.0.1.  Unfortunately I can't find the link describing this solution to give credit but if anyone does find it do link in.
Hope this helps you.