No quadrilateral with 2 internal right angles can be anything other than a square or rectangle. The shape described in the question does not exist.
Improved Answer:-
It could be a trapezoid with two right angles, an acute angle and an obtuse angle.
It is a convex quadrilateral, as the remaining angles could be any two angles with a sum of 180 degrees.
Any quadrilateral in which at least one (and therefore at least two) angles are not right angles is not a rectangle. The majority of these do not have a specific name.
Both a 'kite' shape and a right-angled trapezium can have exactly two right angles
An irregular quadrilateral doesn't need to have any right angles. It's possible for it to have one or two right angles, but no more than two of them.
A kite can have exactly two right angles.
A rectangle.
It is called a Rhombus.
A 4 sided polygon is called a quadrilateral. Depending on where the two right angles are, would put the quadrilateral into different subsets. For example if the two right angles are on adjacent corners (and the other 2 angles are not right angles), then it is a trapezoid. If the 2 right angles are in opposite corners, and the other 2 angles are not right angles then it would be a kite-shaped quadrilateral.
A Rhombus
none
A, a triangle
trapeziod