The fastest method here starts with the Edit button in the top left corner of the main Messages screen. Tap that, and in addition to the yellow pin icons next to unpinned conversations, you’ll see minus icons next to pinned ones. Tap a minus icon to unpin a chat. Again, this is most useful for bulk editing because you can add and subtract pinned discussions at will as you go.
The other choice is to long press on a pinned chat and select Unpin. You can only edit conversations one at a time this way, and you won’t be able to immediately replace an unpinned one with a new one. And watch out: your brain may trick you into thinking the bright red Delete button is the one you want—it’s not. That will, of course, trash the whole conversation for good.
Source : https://www.popsci.com/diy/pin-messages-ios/