Contacts on iPhone don't match Mac

When I use iMessage on my Mac, even though I am on the iCloud, my contacts won't show up by name like they do on my iPhone messages. I have checked the suggestions from the older posts around 2013, but some of the menu items are out of date and don't match up with current mac/iPhones. Also, even though I have the Contacts box checked in the iCloud, my Contacts on my Mac do not include all of my contacts from my iPhone. Thank you.