What is the battery voltage when running above 2000rpm? You should generally be above 13 volts. If not, first is to check battery. Charge it and check voltage. Then let it sit overnight and check again. If the voltage holds, then the system is at fault. It is entirely possible to have a bad reg/rect even if it is new.
If you have a manual, check the stator for continuity. As a simple thing, check the connections. Those connectors could just be dirty enough to not allow things to charge right.
The ride IS the adventure. The destination is just to get gas!