Check to see if it is really overcharging with a voltmeter. It shouldn't be getting above 14.6 or so. If it is hitting 15 volts or more when you rev the engine up it definitely has a problem. The voltage regulator is the most likely culprit. A flakey battery (sometimes hard to confirm) or a wiring problem is possible, but highly unlikely.
Doesn't your new alternator have a warranty?
