There's no formal name (like for triangles there is scalene, etc.) except it is a quadrilateral. A kite could fit these parameters, but there are a number of quadrilaterals which are not kites which also fit the description.
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a parallelogram is a quadrilateral with four parallel sides. a trapezoid is a quadrilateral with two parallel sides.
A shape with four non-parallel sides is an irregular quadrilateral. If the quadrilateral is bilaterally symmetrical, it is a deltoid (kite shape).
A quadrilateral in the shape of a kite has no parallel sides
There are quadrilaterals that have no parallel sides. (basically, a quadrilateral is just any enclosed shape with 4 sides) But all quadrilaterals have angles.
Any shape with four straight sides is a quadrilateral. A trapezoid has one pair of parallel sides, and a parallelogram has two pairs of parallel sides. So any shape with four straight sides and no parallel sides is a quadrilateral that is not a parallelogram or trapezoid.