If I started writing about the history of IH I would be here for months.
The best way to answer your question is suggest to you to buy some of the good IH books out there. The best and accurate authors are Guy Fay, Ken Updike, Ralph Baumgartner (sp), Wendel etc.. The Pribbs books have pretty pictures but many of the facts are wrong and most of the pretty "restored" tractors are not accurate.
Many of the names used are not just a time line. Many of the names occured at the same time. It would take a whole book to go into depth and then we still wouldn't be completely right.
Here in the states generally Farmall was used for row crop tractors, International was used for industrial type tractors. In Europe many of the tractors were badged both McCormick and International on the same tractor.
The name CASE was never used. Case is a completly different company.
The name Case-IH came after IH sold off thier ag division.
There is a great article in the last RedPower magazine by Guy Fay on this topic.
Today there are really only about 3 big tractor manufactures: JD, Fiat (Case-IH, NH, and others) and Landini (McCormick and others).
It gets very complicated about who owns who, as many companies were sold to meet the laws of the European Union. A guy could write a book on this but then by the time you published it everything would be wrong.
As you can see your simple question has a very complicated answer.
If you want to know when the changes came for the Cub tractor we could get that narrowed down somewhat close. The naming committee decisions are on file at the McCormick-IH Collection at the Wisconsin Historical society. The naming decisions are not on the web yet but the paint committee ones are. You can find links to thier websites through
Chapter #4's Website http://www.ihwisconsin.org
We also have over 2,500 images of IH related stuff.
Good Luck with your research.