Rayman had likely received his name after the workings of his body mechanics, in which his lack of arms, legs, and general such limbs would be due to the fact that his other extremities (hands, feet) are projected outward from the core of his body through the use of energetic beams that are naked to our eye. What beams, you ask? This is clear and evident in his name, RAYMAN. So, in giving an explanation behind these particular invisible beams in his anatomy...
"RAY-MAN"...he uses the projection of man, or rather, tiny microscopic men, to aid in the manipulation of his body.