how to suspend getting messages on iMac

Open the Messages app. Open its settings. Click on the iMessage tab. Sign out.

Do you mean notifications from Messages.app (e.g. iCloud Messages and SMS text messages via your cellphone), or do you mean all notifications from all applications?

Also, do you mean temporarily? or permanently?

the specific answer to your question will depend on the above.

At the highest level, System Settings -> Notifications lets you determine which applications can and can not post notifications on screen (as well as the style of notification, and if sounds are permitted). This is your 'permanent' (at least until you change it) setting both globally, and on a per-application basis.

If you just want to suspend them temporarily (e.g. you're in a meeting or need to focus for some time), then you can use the Focus feature to set a temporary state. Use System Settings -> Focus to see/change the current focus categories, and use Control Center (or the icon at the right-end of your menu bar) to toggle which focus state you want.

If neither of those meet your needs, please post back with more details of what you're trying to achieve.

You're welcome. 🙂