Try "hair rooting (punching) tool".
I don't know if there is a specific tool. I have always made punches like this out of a needle pushed into a cork or piece of dowel, then cut off the top of the eye and filed the prongs sharp.
Yeah, there is no tool specifically made for it, by manufacturers or anything, it's something that has to be made. And I don't know of a definite name for it - generally I guess it would be called a hair punch.
If you're interested in how they're made, basically you just take a large sewing needle and stick it into some kind of wooden handle, you probably need to use pliers or hammer it in a little to get it in deep enough to stay. Then you grind off part of the 'eye of the needle' on one side so you end up with a hook shape there. I don't remember if there's more to it, or any specific things I've forgotten that are important. If so maybe somebody can add that info?
I just did a quick search for "hair punch for foam latex" and found a few interesting links:
Thank you guys! It is really very helpful.
SFX people refer to "hair punching", though hobby doll-makers call it a "hair rooting tool". You can find them on eBay at low cost, but as others have said here you can make one yourself.