How to name and cite different versions of Microsoft Kinect?
It is commonly called Kinect V1 and V2. In the research community, it is widely accepted, just because it is their name, example here. 

Note that it is not the true name, as you stated. The best thing I could think of, is to highlight at the beginning of your article (or in the part you spoke about Kinect) that Kinect V1 refers to Kinect for XBox 360 and Kinect V2 refers to Kinect for XBox One (note there is a standalone version for Windows).