Kagamine means "Mirror Sound"; Kagami 鏡, mirror and 'Ne' 音, sound.
The name Rin (リン) has many different meanings and without Crypton making an official statement the given answer here is an assumption. The name Rin could be reference to the Kanji form of "Bell".
The name Len (レン) does not appear to have Japanese origins, so again, the answer will be an assumption. Sources online state that Len means "Lion strength" or general reference to a lion. Rin and Len were said to be based on "right" and "left" according to Asami Shimoda.