On your Mac computer:
- Open a Finder window.
- Go to Applications.
- Find your Messages app.
Conversely, you can use Spotlight search. Just search for "Messages."
From the Messages app on your Mac, you can make adjustments to how your iMessages and messages function and interact between your iPhone and Mac.
In the "Messages" screen, select iMessage from the menu bar.
Other things you can do in the iMessage screen is sign in and out of your Apple ID, change the phone number for your iMessages, choose to send read receipts for iMessages, and of course, disable iMessages completely.
Under your Apple ID, uncheck "Enable Messages in iCloud".
Finally, open the Notifications & Focus pane in System Preferences. Select Messages from the sidebar and toggle "Allow Notifications" to the off position.
Now, you'll no longer receive message and iMessage pop-ups on your computer. All your messages, however, will still show up on your iPhone or Apple watch.
Hide Alerts in iMessage for a certain contact or number
If instead you just need to stop alerts for a certain number (maybe a particularly annoying one), then you can simply:
- Right-click the person's number in your Messages app.
- Select Get Info.
- Check Hide Alerts.