Short answers, pulled from the story.
Elkin Mathews and John Lane opened a shop in London to trade in rare antiquarian volumes in 1887. The partners chose the name Bodley Head from a bust of Sir Thomas Bodley that sat above their door.
Allen Lane departed in 1936 to found a new company known as Penguin Books after inheriting control of the firm from his uncle John Lane in the mid-1930s. He published the first Penguins under the Bodley Head imprint in 1935 before leaving.
George Bernard Shaw contributed works to the Bodley Head catalog during the mid-twentieth century while Graham Greene wrote several books under this imprint before his death. Charles Chaplin also published titles with the company alongside William Trevor and Maurice Sendak created illustrations for children's books distributed by the firm.
Random House purchased The Bodley Head in 1987 along with sister companies Jonathan Cape and Chatto & Windus. The new owners used the name primarily for children's books until April 2008 when they repositioned the imprint as an adult non-fiction division within Vintage Books.
Archives of The Bodley Head Ltd remain stored at Reading University today. Margaret Stetz and Mark Samuels Lasner documented the history in England in the 1890s published by Georgetown Univ Press while J. W. Lambert and Michael Ratcliffe wrote The Bodley Head 1887, 1987 covering the full century of operations.