i wouldnt say it was a cursor ..
i presume you mean the marker that flashes pointing out where you are about to type.
honestly if it has a name i dont know it, why not give it your own personal nick name, im going to call it TextTypingPoint
Edit: huh nevermind , apparently it was a Command Promt Location Marker. its basically stuck with the world of computers as we have moved forward past the days of command line interface and now its used as a generic marking for 99% of text.