According to Stokes Iconography of Manhattan Island, on October 8, 1908 a city ordinance was passed changing the name of Blackwell’s Island Bridge to Queensboro Bridge.
Further research into Stokes Iconography provides more history about the Queensboro Bridge.
The city began proceedings to acquire the land on April 25, 1900. On November 15 the common council passed “an ordinance to provide for the construction of a new bridge over the East River between the boroughs of Manhattan and Queens.” On February 23, 1901 the plan for the construction was approved. “The bridge is to be constructed on the cantilever principle, is to be 150 feet wide and 2,710 feet long, and is to cost $5,740,000.” Construction began in July. On March 18, 1902, the Board of Alderman passed “an ordinance naming the bridges across the East River. This provides that: 1, the New York and Brooklyn Bridge shall be designated the Brooklyn Bridge. 2, the new East River Bridge shall be designated as the Williamsburg Bridge. 3, Bridge No.3, crossing the East River, shall be designated as the Manhattan Bridge. And 4, Bridge No.4 crossing the East River shall be designated as the Blackwell’s Island Bridge.”
(FYI: the entry following the March 18, 1902 entry in Stokes has nothing to do with the bridges but it is the kind of interesting and quirky information that this reference source is full of: “April 1902 – About this time ping-pong had the vogue that Mah Jong came to have in 1920 and the cross-word puzzle in 1924. – Sullivan, Our Times (1926).”)
In January 1907 the proper approaches were planned, with the commission recommending a “diagonal approach to Blackwell’s Island Bridge from Second Avenue to 57th Street; that the street car tracks on 59th Street be depressed under Fifth Avenue, and that 60th Street be widened by 100 feet.” On October 8, 1908, as mentioned above, the name of the bridge was changed to Queensboro Bridge, which officially opened on March 30, 1909.
Coincidentally, 58 years after the name change, almost to the day, on October 10, 1966, this album was released with a catchy song that used the colloquial numerical name of the bridge in the title.