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You cannot have a 2d pyramid - whether or not it is square based. The 2d cross section will depend on the plane of the cross section.
A square-based pyramid net consists of a square base with four isosceles triangle faces extending from each side of the square. The triangles meet at a single point at the top of the pyramid. When the net is folded and assembled, it forms a three-dimensional square-based pyramid shape.
The net you are referring to is called a square pyramid net. It consists of four triangular faces and one square base. When the net is folded along its edges and assembled, it forms a three-dimensional square pyramid shape.
It is simply called a square based pyramid
A triangle and a square