why does one of my contacts have a half moon against their name

It means the donot disturb is turned on for that contact.

It's either done in purpose or accident.

To turn it off , you must go to messages for that person,

Touch the little "I" icon on top right, and slide the donot diturb bottom off, it's one of the ways to do it.

Cheers.

Hello. In OIS 11 the solution is to swipe the message to the left. You will see "Hide Alerts" if the sender is NOT blocked. To block the sender touch the "Hide Alert" and change it to "Show Alerts". The half moon will show and messages sent will not alert you, but you can see them later on your list of messages.

That quarter-moon icon means that particular contact is on "do-not-disturb" mode. Click on a message from that contact and then click Details in the top right. You'll see the "Do Not Disturb" button on that page - click it OFF (white side showing) - the quarter-moon icon will then disappear and all will be back to normal.

I am having the same problem but i do not have a details i have a question mark and it doesnt work

Would this be the crescent moon something called -Do Not Disturb- This makes it so that no notification sounds, phone calls, and text messages, calendar and reminder alerts don't disturb you whether you iPhone is locked, off, or on the main home screen or even when you are in apps.

Open message. Then tap in upper right corner information. Check to make sure the slider for hide alerts is off.

Also on some messages you might see a do not disturb turned on

Either case they should be off or you will see the half moon but will not receive alerts.

Because you have do not disturb set up for that contact in messaging.

Open your message app with that person - select details - uncheck do not disturb.