From Long Island City by Thomas Jackson & Richard Melnick:
Cove was the site of a Native American settlement. Fresh water came
from a small stream, later called Linden Brook, that flowed along
Astoria Park South. Here, they cleared woodlands to grow corn,
harvested oysters and clams, and caught fish.
Linden Brook is hard to find on maps. Apparently it was a small
stream, and by the time the area was settled enough for good maps to be
produced, it had mostly disappeared underneath urbanization. However,
the 1873 Beers maps of Long Island City and region show it, though just
barely. Below is a large section of the map. Pot Cove is the area
directly below Hell Gate and Ward's Island, above the spur of land that
juts out above Hallet's Cove.
Below is a closer crop of the Pot Cove area. The Linden Brook is visible as a wavy line in the upper right, below Linden Street.
And below is a very close crop of the area; Linden Brook is the wavy
line on the right, and outlets into the water on the left. Linden
Street, obviously, is named after the brook; today this is the line of
Hoyt Avenue and Astoria Park South.