No one answered! But now, I have an answer. Comments are welcome...
The name 'immersion lens' came from the classical light optics. Ion optics, behave in the same way as classical optics with refractive index replaced by square root of electric potential (if we use electrostatic field as lenses). So, in Ion optics, many terms and names are adopted from classical optics.
Immersion lens: It is a two electrode with some potentials on it. It act as a lens to focus ion beam/electron beam. The energy of the particle at the entrance and exit are not the same. It is similar to an immersion lens in classical optics, where one side of the lense is immersed in another medium. Here, the refractive index at the entrance and the exit are different. So, an electrostatic lense with two electrodes with a field in between act similar to a classical optical lens with the refractive index at the entrance and exit are different. Hence the name 'immersion lens'; same name adopted in ion optics as well.
Einzel lens: This is basically a 3 lense system (it can be 5, 7 or more lenses), with entrance and exit potential same; in general with the entrance potential same as the potential of the source (or the electrode which extracts the ion/electron beam to the einzel). Here, as the entrance potential is same as the exit potential, the energy of the particle entering and exiting the lense will be the same. This system acts like a normal classical optical lense (either converging or diverging). Normally, Einzel lens are used to focus the beam.