"Turns as" means the consist serving as a given train is serviced and goes back as another. In the case of the former "Night Owl", 65/66/67, the consists were captive to that service, so 65/67's consists were turned at Washington as 66 and not some other regional. Now, since 66 originates in Roanoke and 65/67 terminate in Newport News, that patten has been changed, and AmtrakBlue noted what the turns of 65/66/67 are now.
As to the rest of your question, train names/numbers are not determined by what equipment make up their consists for any given run, but by the schedules they run and the stations they serve. If a consist that ordinarily runs as a Vermonter, or one that looks like a Vermonter, is pressed into service as an NE Regional for some reason, it will have a NE Regional train number and name. It isn't a Vermonter "train", it is a consist used ordinarily as a Vermonter. If it isn't running the Vermonter's schedule, it isn’t a Vermonter.
As it stands, I still say you have a 65 turning as 186, with 65 having "Night Owl" type consist including an Amfleet cafe/BC car. Both trains are branded as Northeast Regionals. While most NE Regionals run the same consists, there is no rule demanding that be so. 65/66/67 have always had different consists from the other Regionals and now the trains they turn as do as well.
I'd be interested in what the equipment rotation is since 65/67 terminates in Newport News and 66 originates at Roanoke. I could probably deduce a likely one by examing NE Regionals schedules, but am not so interested as to bother. Also, since 65/66/67 temporarily terminate/originate at New York, I wonder what the rotation will be once they are extended back to Boston in the Fall.