A quick test to see if the alternator is functioning is to use a VOM. Measure battery voltage with the engine off. remember.
Start the engine and measure the battery voltage. Both measurements should be on the battery terminals at the battery.
With the engine running the alternator should produce voltage above 13V. More likely 14-14.5. If the battery voltage is not increased from resting battery voltage, there is no alternator output. No output can be due to the altenator, regulator or the wiring between.
FWIW, many 're-man' alternators re-use the regulator. Makes me wonder, why do they think these alternators were returned as cores in the first place? To test them in a re-man shop is not the same as testing them connected to a vehicle. IMO.
I would not buy a 're-man' that re-used the regulator that was 'tested good'. Too much labor in the EMTs.