Hello dinkiesteach,
Thanks for using the Apple Support Communities. We understand that you're running into issues with your Contacts names not appearing as expected in Messages on your Mac. If you haven't done so yet, give the following actions a try and see if they help.
- Open system preferences, select Apple ID in the top right corner
- Select iCloud in the left menu
- In the list of "Apps on this Mac using iCloud", uncheck Contacts
- Wait a few minutes…
- Check contacts again, a "Setting up…" message will appear to the right of "Contacts" for a few moments
- You should begin to see the missing contact names appearing in Messages
Let us know if this helps.
Best regards.