It is not uncommon for an alternator to be bad even though it is “new”. You can take a simple volt meter to the battery and check the voltage output. You should show 13.5 volts at idle.
I do not know the way to check just the regulator since it is built into the alternator.
The cause of them to go bad is usually complicated but there is a short and or back feed into the alternator. If you have aftermarket stereo equipment with a high-powered amp it can cause this problem as well.
Edgewood Auto Parts #253