I think they call it an "integral part of the course." Probably designated as such, as you said.
I played a beautiful private club, William Flynn design, several years ago. Standing on the tee of this one hole, about 290 yards out, sat this beautiful, old-time water well with the little gazebo roof and everything, with this old vintage flat-rock circular base, about four feet high, that surrounded it. Very pretty, even from 300 yards away.
I remarked to the guys in my group - "it's beautiful, but it's also odd that it would be dead-center of our fairway."
It was well out of reach for me, even if I did happen to find the center of the fairway. But one of the guys piped his drive, and the contour of the fairway sloped right-to-left, and he hit a pretty good draw. I knew he'd end up being pretty close to it.
So we get down there and sure enough - his ball is about 10 feet directly behind this thing, between his ball and the hole. We checked the scorecard in hopes of seeing a local rule established about it. Turns out (afterward in the bar someone told us) this well-house was part of the property some 150 years earlier, and they decided to maintain its legacy. The note on the back of the scorecard said, "water well on hole 7 (or whatever hole it was, can't remember) is considered an integral part of the course, no relief provided unless the object impedes stance or swing." In other words - he wasn't getting relief simply because the thing sat between his ball and the green.
He still had 170+ yards, uphill to the green for his second shot, but had to intentionally miss the green to the right to avoid hitting the well-house.
Beautiful hole, beautiful landmark, but an utterly senseless rule given the circumstances.