It could not have been called Long Island Valley because:

The global sea level was about 150 metres lower during the
peak of the last Ice Age, and was at its lowest about 20,000
years ago. The sea was below its present level from 100,000
to 5,000 years ago.

Human beings, and all the normal vegetation and fauna of the
neighbouring land-mass, extended onto the continental shelf
during the period when the sea level was lower than at present,
that is roughly from 100,000 years ago to 5,000 years ago.

When the sea level rose again, while the ice caps were melting,
vegetation was killed off by salination and inundated (gradually),
while animals and people who had been on the continental shelf
moved back onto the continents where they joined the people
who had been living there anyway.

Flood myths that occur all over the world are the "folk memory"
of the experience of suffering 10,000 years of (slowly) rising sea
level, and the continuous loss of hunting and foraging territory.

[Who knows how fast the change really occured?]

There is a continuing need to discover, categorise, and date more
prehistoric archaeological sites offshore. Work by amateur
archaeologists and chance finds by trawler fishermen, scuba sports
divers, and sponge divers who may recover stone tools from the
seabed can be of great importance.