Previously I commented that sites were prematurely using the word "overdrive" to describe these charged up modes and that there was no official source for it, but that has changed now with the Pokémon Daisuki Club's page on Kyurem. As you can see in the picture (but possibly not read), it says "This is what the Overdrive body is!". The captions read "Shining Blue 'Black Kyurem'" and "Burning Red 'White Kyurem'". On a previous page it reported that these formes occur when Kyurem's emotions are running high.
Fun little tidbit for the night Thanks Taylor for the tip about this!
<3 pokejungle