In old old days a Wood Well covered Design was more a common place ..to protect the well from contaminants … now seen in old western movies. Today a covered well structures is more of a decorative feature, or as a way to hide your new well head pipe which sticks out of the ground in the front yard.
A covered wood well can be referred to as a wishing well because tradition had it you would through in a coin into the well and make a wish.