What's the name of this electrolysis device? I've seen it in a couple of videos, it's used to electrolyze water in 2 different containers at the same time to make a comparison and thus is very handy.  

What is it called (besides just a hydrolizer)?
Based on this article, in which the authors describe a system that can do 25 cells simultaneously, the term 'Parallel Electrolyser' would seem appropriate.