A trapezium, possibly "trapezoid" if you're in USA.
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Only if it is a trapezoid (US usage) with one set of parallel sides, or a parallelogram with both sets of opposite sides parallel. The term quadrilateral only means that the shape has 4 sides.
Only one quadrilateral has only two parallel sides: the trapezium.
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.
Any four-sided shape is a Quadrilateral. Square, Rectangle, Parallelogram, rhombus, trapezoid etc. It may have no parallel sides as in a kite, 1 parallel side as in trapezoid or 2 parallel sides as in parallelogram.
A quadrilateral that has only one pair of parallel sides (the other pair not parallel) is a trapezium.