It appears that IH wasn't used as make name. Except for the brochures of the 1910-1912 Roadster, all documents use "International [name of the truck]" as title, and "IH" or "IHC", when present in the inner text, is more used the way"GM" would be in the Chevrolet or GMC literature.

When looking at trucks' logos, the "International" badge is clearly separated from the IH/IHC one (once again, when present), so this latter should certainly just be seen as the one of the parent company. More or less like the Iveco badge that was present on Fiat, Magirus, OM or Unic vehicles in the late 1970s / early 1980s.
See, for example, here (1947-49 KB-6), here (1963-70 Loadstar CO) or here (1971-84 Transtar 4200).

And even data plates seem to support this (at least pre-WWII to mid-1960s ones).

I really dislike the way the initiator of this change in WP promote this move (he apparently often harass people that disagree with him), but his argument makes sense, and reflect what can be seen on the trucks, in books and in a lot of sites.


(As usual, click on a picture to get a larger version)