"East Village" became a popular term in the 1960s. The East Village Other (a radical publication of its period, with much information about Dr. Timothy Leary and drug culture) began its brief life in late 1965.
A Google Groups post to alt.fan.laurie.anderson on 19 April 1994 has both "EV' and "LES": "And there's a lot more than those folks, too; the LES/EV scene is one of the most complex and cross pollinated New Music scenes in the world at present."
9 December 1959, New York Times, pg. 60:
One student, whose stomping ground was the East Village, felt his finds - tinted cordial glasses, bone spoons and stainless flatware from Merrill Ames - were the most elegant designs in the Pratt show.
17 July 1960, New York Times, pg. 222:
SPEAKING of paperbacks, the Paper Book Gallery, which has had a couple of shops in Greenwich Village long enough for them now to be considered landmarks, has a new place in the East Village - Third Avenue, near Cooper Union.
21 June 1964, New York Times, pg. 6:
In recognition of the shortage of family-sized apartments in the Greenwich Village and East Village sections, more than half of Village View's suites contain two or three bedrooms.