Well, first of all, it was the official name given by Chevrolet for its 1955-59 trucks, as you can see for '55, '56, '57, '58 and '59 (even if I suspect the 1959 picture writing to be a later modification)

If you search for "Chevrolet Task Force", you'll find what is called "Chevrolet Apache" in IMCDb:
- Flickr;
- Duckduckgo;
- Bing;
- Ggle.
All links give the 1955-1959 model years for these trucks.

And when searching for "1955-1959 Chevrolet pickup trucks", it gives you easily sites saying "Task Force" in the first line. Ok, some times, you have to go to the third paragraph to see this name

So yes, I think the "Task Force" name meets the "well known name" criterion
You know my point of view: I prefer accurate names to vague ones. So I think we had better to gather all 1955-59 trucks with the same name and "3100 & Co" as complement.
As we both agree : we must find another name for 1955-57 Chevrolet pickups, as "Apache", "Viking" and "Spartan" names didn't exist at that time. So if we give them their real "Task Force" name, why not give it to other TF trucks?

And for 1960-66 models, they all belong (1960-61 Apache included) to the 1st generation C/K-Series, which starts only with the 1967 models in IMCDb (except one single lost 1966 model since this afternoon ).