Block messages in Messages on Mac
If you use iMessage to send text messages, you can stop receiving text messages from certain people.
In the Messages app on your Mac, select a conversation.
To search for contacts and content in conversations, click in the Search field in the top-left corner and enter what you’re looking for. Or, choose from the suggested contacts, links, photos, and more.
If you’re restricted to sending and receiving messages with only certain people, an hourglass icon appears next to those people you can’t send messages to.
Choose Conversations > Block Person, then click Block.
Tip: Another way to prevent unwanted people from bothering you is to set up communication with your contacts only.
To view and manage your list of blocked phone numbers and contacts, choose Messages > Preferences, click iMessage, then click Blocked. See the Apple Support article Block phone numbers, contacts, and emails on your iPhone, iPad, or iPod touch.