It's not really necessary to ...

It's not really necessary to verify the pump speed.  You are testing an integrated pump and driver unit (pumpset), so the key performance parameters to verify are the head, flow and power consumption curves, which must be within factory-stated tolerances, assuming that your power supply is also within specified tolerances.

On your table, I believe "motor data" just means reading that number off the pump curve, e.g. if you have a 50 Hz power supply, the pumpset will run at a nominal 1,450 rpm (or whatever speed is stated - this will just be the motor speed at the rated load) and it would be 20% faster for a 60 Hz power supply.  I think that "vibration data" refers to measuring vibration at the motor bearings and analysing the frequency - there will be a vibration at the vane passing frequency (for conventional vaned impellers, not vortex pumps), so the rotating frequency can be calculated by dividing this frequency by the number of impeller vanes.  However, as I said, it is not really important to know the pumpset speed because what it is guaranteed to deliver is the stated hydraulic and electrical performance for a given power supply.

If you are using variable speed control (VSD/VVVF drives), test using 100% speed.  In any case, factory data for reduced speed operation or reduced impeller diameter is often simply calculated using pump affinity laws.

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I've realized that I might have made an incorrect assumption:  I interpreted your comment about close-coupled design as referring to single stage submersible pumpsets with motors sharing the same shaft as the pump, as per submersible sewage pumps.  For multi-stage submersible borehole pumps, you are not necessarily purchasing an integrated pump and driver, so the motor design is not the pump manufacturer's, and it will also probably be almost impossible to derive motor speed from vibration data.  However, speed is again not critical to measure because correctly sized/rated motors of the same basic design (e.g. 2 pole or 4 pole) and efficiency will operate at similar speeds (certainly within the 5% tolerance typically quoted for flow performance data), and some pump manufacturers even simply denote the operating speed on the performance curves as either 50 Hz or 60 Hz.