Bar graph polyomino
A bar graph polyomino is a semiconvex polyomino that contains one side of its boundary box orthogonal to its convex axis (for example, a row-convex polyomino that contains a vertical side of its bounding box). Equivalently, it is a polyomino that are directed from two adjacent corners.
Since they are both directed and semi-convex, bar graph polyominoes are a subclass of directed semiconvex polyominoes.