V2 is the minimum speed at which you can climb up to acceleration height, having lost an engine. It represents neither best angle nor best rate of climb but is a compromise 'minimum stagger away from the ground' speed that acknowledges that selecting a low pitch attitude to accelerate to best angle of climb speed after an engine failure would leave you with less vertical clearance from short range obstacles in the early climb.
Not knowing the B737, in general the all engines climb speed is V2+10, it may be V2+15 for the B737. This represents a speed that is easier to hold on all engines without extreme pitch angles and is closer to best angle of climb. In general the advice is that, although if you have an engine failure below V2 you should accelerate to and climb at V2, if you have an engine failure between V2 and the all engines climb speed you should hold the speed at engine failure, and this includes any emergency turn below acceleration height. In this scenario reducing to V2 would do nothing for you, it would reduce your climb angle and bring you closer to the stall. Is the 737 operated differently to this?