I had a background check for an investment bank I worked for this summer and the things they will screen you for are:
- Address history in past 3-5 years
- No Criminal Record claim (which they can cross check with other authorities)
- Current Address proof
4.Educations certificates ( I didn’t have to give my uni one since I haven’t graduated but they might ask for a reference letter instead)
Not sure how Kroll works but these are the 4 main things.
As far as references are concerned, I think it is not necessary to give the ones you mentioned on your CV but if you did put em down, they should be ready to write you one.
They usually ask for 1 referee but at times they might want one academic and one from a previous employer.
Hope this helps!