As Tenpenny said above: pumps are initially designed around one point, and only one point. That is, one capacity and TDH at one speed. Every deviation moving away from that design point creates flow instabilities; very minimal near the point and increasing the farther away you get. Unless otherwise stated in the contract (very seldom), manufacturers will only guarantee the pump to operate at ONE POINT. It may not be the same point the pump was designed for, but they will only guarantee ONE POINT.
Most manufacturers do not test individual pumps at the actual point they are sold for, the "rated", or guarantee point, unless requested by purchaser. Typically they will be tested at full impeller trim at 3-5 points on the curve, and speed many times is dictated by whatever test stand motor is most easily accessible. The affinity laws are then applied to test data and necessary corrections applied to impeller and/or case, such as trimming, backfiling, cutwater adjustments, etc.
In most cases (standard services), pumps are not even retested after these adjustments are made; just reassembled, painted and shipped. For 90% of pumps sold, this is satisfactory. For critical service pumps, however, most will be retested until test data is "jam up".
Of course the purchaser can require any testing parameters he wants; up to being witnessed, with the actual job motor, and also can call out spec at rated Conditions of Service, and as many other points/speeds as he desires to pay for.