By "independent flash" I mean a flash which is not attached with the camera by default. What is the technical name for it?
It depends on the actual type of flash unit. If it's the kind of flash that fits on the hot-shoe on top of the camera, then it's usually called a flash-gun or a speedlight.
If it's a 'professional' flash of the type used for studio modelling shoots, it's usually called a studio flash.
The catch-all term for any flash not on the camera is off-camera flash.
If you look online at places like B&H and Adorama, you will find that lighting that is not attached to a camera is referred to as Strobes. On camera lighting is often referred to simply as a 'flash'.
Monolights are all-in-one strobes, combining the power, control and flashing bits in one unit. When separated, they are called 'heads' and 'power packs'.
Flashes are often referred to as 'speedlights' though this is simply what Canon and Nikon use in there product names.