Such a shape cannot exist.
It's a parallelogram.
That would be a trapezoid. A trapezoid does not have to have two right angles it only needs to have two parallel sides. There is not a name for the exact quadrilateral you are looking for but the shape is still within the definition of a trapezoid.
There are quadrilaterals that have no parallel sides. (basically, a quadrilateral is just any enclosed shape with 4 sides) But all quadrilaterals have angles.
The shape you are looking for is a quadrilateral. If you have a square, all angles MUST be right angles. A parallelogram can also have 4 equal sides in length and parallel sides, but a parallelogram doesn't have right angles.
A shape with parallel sides but no right angles is called a parallelogram
No shape has only 1 parallel side. A trapezoid is a 4-sided shape, or quadrilateral, with only 2 parallel sides; it does not necessarily have to have 2 right angles. (In the UK a trapezoid is called a trapezium.) In North America, a trapezium is a quadrilateral with 0 (no) parallel sides.