In two dimensions, all sorts of triangles. In 3 or more dimensions there is no specific name for shapes with three vertices.
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2-dimensional shapes, with three straight sides have three vertices.
Shapes that have fewer than 5 vertices include triangles (3 vertices), quadrilaterals such as squares and rectangles (4 vertices), and circles (0 vertices, as it is defined by its center point). These shapes are classified based on the number of corners or points that define their boundaries. Shapes with fewer vertices are typically simpler in structure and have fewer sides.
You can find a polyhedron with any number greater than 4 of vertices or faces. However, a torus, ellipsoid, sphere, paraboloid, hyperboloid are all standard shapes with no vertices. Cylinders, too, have no vertices. And there are many completely random shapes - a lump of putty, for example, which will have no vertex.
In 2 dimensions, a quadrilateral. In 3 dimensions, a tetrahedron.
A triangle is the only polygon with 3 corners (vertices). There is no polyhedron with 3 corners.