I have done parasitic current draw tests on lots of vehicles, and it's not uncommon for the internal voltage regulator to draw a few milliamps of current on a continuous basis. A good condition battery with a full charge should sustain a tiny current draw like that for several weeks without losing enough charge to keep the engine from starting, so it's possible your new alternator is drawing too much current, or the battery might be on the verge of failing. A well-charged battery in good condition should be able to support a load test of 1/2 the cold cranking amp rating for 30 seconds, and maintain at least 9.6 volts with the load still applied. For instance- - - -a 500 CCA battery should test at 250 amps for 30 seconds, and the terminal voltage should be 9.6 Volts or more before the load is removed. A quick and dirty load test for folks without a formal tester- - - - -turn on high beam headlights, blower motor, etc., disable the ignition, and crank the starter for about 15-20 seconds. Battery voltage should not drop below about 10 volts at the end of the cranking session.
One little tip- - - -the starter isn't bulletproof, so only run that kind of test once, then allow a cool-down period of several minutes.
Jerry