The name come from from that fact that these are absolute return funds, and they usually hedge hedge against market movements so their performance depends on their strategies and not market movements. This does not make them less risky: in fact, they are very volatile investments.Market neutral means one risk is eliminated, but hedge funds take many others.
Hedge fund managers' fees (and individual mangers remuneration) is usually strongly tied to performance. Typical fees are a (fairly high) proportion of the gain.
The growth in both hedge funds and index trackers, taken together, is somthing of a change in how investors invest. Rather than putting money in moderately active investments, some investors have switched to favouring a mixture of passive and extremely active investments.
This makes the high fees (compared to ordinary active funds) charged by hedge funds look more reasonable. They are offset by the low fees (compared to active funds) paid on index trackers.