Which US universities publish cohort ranking - position in class? For example when you take the GRE you get the percentile score, is there such statistics and how is it called? Do US publish such data or does it have to be asked specifically?

For example you are in a committee and have to evaluate how applicants performed compared to their peers during their bachelor or master's degree. For example in the UK first honors is around top 9% of the cohort.
The US has no organized system of class rank comparisons. Some individual universities (or departments within a university) may track this, but at the university level the educational approaches are so diverse, even for different options within a single department, that direct rank comparison would make little sense in any case. It is for this reason that a number of high ranked universities (MIT being one example) explicitly refuse to create such ranking comparisons.