It's called "Tudor City" after the architecture and, well, that's the name the developer gave it. The first apartments rented for $500 (a year!).
18 December 1925, New York Times, pg. 1:
TUDOR CITY TO RISE
ON 5 EAST SIDE ACRES
Tract Near Grand Central
Valued at $7,500,000 Bought
for $25,000,000 Project.
TO BUILD TWENTY UNITS
Apartments to Rent at $500 a
Room - Hotel, Heating Plant
and Garage Planned.
As a site for the largest housing project ever undertaken in mid-Manhattan the Fred F. French Company, operators and builders of New York, announced yesterday the purchase of about five acres of land and buildings in the old Prospect Hill section adjacent to Forty-second Street and the East River.
The project, which will involve many millions of dollars, calls for the construction of about twenty units, consisting of apartment houses, hotels, garages and power houses, forming a complete high class community within a couple of blocks of the Grand Central business zone. The community will be known as "Tudor City."
The buildings in the new development will be of the old English style of architecture and will face on parked courts and winding roadways.
It is estimated that the proposed buildings will house about 10,000 people.