If you dont want to recive the notifications or messeges from any person .you can get rid of it by following steps to mute that conservations.
First of all go to Messaging application from your iOS device.
Now find the person you want to mute Once you have found the person Tap on it to open chatting page.
Now on the Upper right of the page there would be a Details button click on it.
On the Bottom of the page there will be options for Do Not Disturb . button trun it on.