The East Village wasn't always called that, it was simply part of the Lower East Side until the mid-1960s. At that time the area — mostly populated by working class immigrants — began changing, with artists moving in after getting priced out of nearby Greenwich Village. This change came with a rebranding, and the new name was popularized by both real estate agents and newcomers. With that, a wave of gentrification created the East Village—a neighborhood that was never officially dubbed that.
In the 1964 guide "Earl Wilson's New York," the author declares that "artists, poets and promoters of coffeehouses from Greenwich Village are trying to remelt the neighborhood under the high-sounding name of 'East Village.'" Around the same time, The NY Times began using the name, and in 1964 reported that the affluent were taking over the area—"When artists and writers began in 1960 to move into tenement housing in what is now called the East Village, the older residents of the Lower East Side greeted them as they had all previous invaders: They fought back." The artists were standing beside those that came before them to "face a new invasion... The uptown rich." And so it goes.
The neighborhood also got its own publications, among them was The East Village Other, which debuted in 1966 (not to be confused with the The Other Paper). While the moniker existed in everyday life, it was never named the East Village in any official way—in the 1990s, a spokesman for the city's Department of City Planning told The NY Times that "while the East Village is not listed as such in city zoning maps, the term has been recognized by City Planning officials for about 25, 30 years."
To match its unofficial name, the area also has ambiguous borders, but that's par for the course in New York, where there aren't any official border lines for any neighborhoods. Kate Cordes at the NYPL told us, "Neighborhoods are just crowdsourced knowledge and boundaries are unofficial."
However, she noted that in a city planning proposal from 1969 some boundaries were offered, unofficially stating: "The East Village lies between East 14th Street and Houston Street from the Bowery and Fourth Avenue to the East River."
We ventured over to Tompkins Square Park recently to ask people on the street to highlight what they believed the borders to be (watch that video here, or below).