I was told that a bus tour guide has joked that it's because the area contains no whores, or "no ho's." Those bus tour guides sure are funny.
Here's an odd twist: "Noho" contains Bond Street, the address of the completely fictional and now infamous "Big Apple Whore Hoax."
NoHo, for North of Houston Street (as contrasted with SoHo, South of Houston) is a neighborhood in the New York City borough of Manhattan, roughly bounded by Houston Street on the south, The Bowery on the east, Astor Place on the north, and Broadway on the west. NoHo is wedged between Greenwich Village, west of Broadway, and the East Village. NoHo is primarily made up of loft apartments, which in turn makes it one of the most expensive and desirable neighborhoods in Manhattan. Its small size and central location also contributes to a high demand, again keeping prices high.
13 February 1972, New York Times, pg. R6:
In a nod to nearby renascent SoHo, some residents call the Bond Street area "Noho," an acronym for "north of Houston."