What are the male pin ends on stranded jumper wires called?
Those are very long, but in general what you are looking for are (at least colloquially) called
 machine tooled pin headers

"Machine-Tooled" generally means it's made with something along the lines of a screw-machine. It's a machining process, rather then a stamping process, as is common for rectangular pins. However, it also means they do cost more.

Off the top of my head, I know Mill-Max makes them, but they are fairly expensive (mill-max is high-end/mil-spec. On the other hand, 1 strip of 40 pins may be ~$5, and considering that would make 20 jumpers, cost may not be too big a deal.




I would imagine that other companies make similar parts, but I don't know them off the top of my head.



Digikey carries at least some varieties of them:


The place to look is the "Rectangular - Headers, Specialty Pin" category.



It's also possible the jumpers are manufactured using the pins from some connector, without the actual connector housing. In this case, you're on your own. I don't think there are really any resources for looking up connectors by their pins.

However, the magic words here are again "Machine Tooled". Machine-tooled pins are the round variety (e.g. they are machined, not stamped or moulded).