How to name and cite different versions of Microsoft Kinect? There are at least two types of Kinect cameras, one is called Kinect for Xbox 360 (https://en.wikipedia.org/wiki/Kinect#/media/File:Xbox-360-Kinect-Standalone.png)
and another one is called Kinect for Xbox One (https://en.wikipedia.org/wiki/Kinect#/media/File:Xbox-One-Kinect.jpg).

First, do they have shorter names (eg. Kinect v1 and Kinect v2) widely accepted in the research community? Moreover, how would you cite them in a scientific paper?

I'm now sure if this question is more appropriate for UX stackexchange or for the academica stackexchange. Kindly let me know in the comments. Thank!
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).