I've been curious about this too and have wondered if there was any parallel with Maiden Lane in NYC. I keep looking. In the meantime, look at the images below. The first is from the 1876 Walker Atlas, the second from the famous 1896 map and the present image from Google. You don't see the "Maiden lane" on either early map. At first I thought the 1896 map showed it but that must be the artist's depiction of Water Street, since Water Street appears on the 1876 map. The lane now exists on the property of Peter Terhune in 1876.
If you look closely, there is a building set back much deeper from Hudson, owned by W. Holly. Presumably, a lane ran back there.
There's a Maiden Lane in San Francisco as well. Here are theories on the naming of
"Maiden Lane" in NYC. The comments that follow are interesting too.
“Tradition had it that the girls of early Dutch days were wont to stroll by the little stream along what was known first as Maagde Paatje,” says a 1911 New York Times article. There is a little stream by our Maiden Lane too.