Handrill is the name sometimes given to it they are sometimes just small hand cranked drills.
It can also be called a pinvice. This one of two things depending on what your school of training is. It can be a small miniture drill chuck that can take drill bits down to rediculous sizes of smaller than 1mm. Or it can also be a small device similar to those watch makers screwdrivers you can get at the thrift mart. You know the ones they come in a pack usually the size of a carton of smokes, they usually look the similar but the pin drill will have a small chuck like part on the end to allow you to put in drill bits.
They are all good for the job. The only real difference is that the screwdriver like one is good for use in the hand, quick or not critical acurate holes and the drill chuck one can be fitted into the end of a convensional drill or drill press for super acurate or depth acurate holes. I have both so I have the ability to do eaither, but you can get away with one or the other if needs be. My pin vise is nearly 40 years old and was my fathers when he was an aprentice tool maker, they just dont wear out, so you only ever need on unless you loose it. Neither should cost you more than a few bucks.