As mentioned earlier it looks a lot like a wire twisting tool. The kind used in a drill to twist electrical wires together before installing a wire nut, or one that could be used to twist safety wires.
I just read through this thread after getting tagged by Ray in one of his replies.
My first thought was a quick clamping pin vise rather than the common threaded cap and collet type. Maybe for a production shop. The hex shank is throwing me off though. It makes little sense if the tool is used in a stationary task. It implies rotation.
I was really leaning toward wire twisting tool as well...but it seems too precisely and well made for such a task. And it doesn't seem like you could easily clamp two or three wires on the fly in a junction box with that tool with a drill attached to it. You would need a third hand making this tool a bit of an unsuccessful experiment rather than useful.
Finally, the tools it came with, it doesn't seem to pair well with those. If this came in a grab bag of tools, I don't know that I would associate it with them. I wasn't there for the unboxing though.
With all that said, I'm kind of back to stationary tool. I was thinking it could be useful for model making, soldering, maybe brazing of fine tools, jewelry of that sort.
EDIT: couple more thoughts...is the hex shank turned and milled into the bottom half of the tool? Or is it pressed into the part? The only other possible use, I could see is a special built tool grinding fixture? That would explain the hex for indexing, as suggested by someone else.