My contacts in Messages are not syncing on my new Mac
You can try following method
- Connect your iphone or iPad to your mac using a usb cable.
- Wait a few minutes and then open a new Finder window.
- Your device should appear in the Sidebar of your Finder window.
- Select your device and you should get a panel like the one below.
- Click on info on the top line of your panel.
This should give you options on which things to sync. This method is described in more detail at this location