The Great Eastern was indeed laid down as the Leviathan. The cost of her launch exhausted the owner's funds and she lay unfinished for a year. She was sold to new owners called the Great Eastern Ship Company who dealt mainly in the Far Eastern trade (hence the change of name). She was built by Messrs Scott, Russell & Co of Millwall, London, with a tonnage of 18,915, comination paddle wheels and single screw with a maximum speed of 13 knots. She had six masts and an incredible five funnels. Her keel was laid on 1st May 1854 and she was launched on 31st January 1858. It was decided that she would be more profitable on the New York run - she had cost $5,000,000 after all! Her maiden voyage was 17th June 1860 but she proved unpopular and became a cable layer four years later. She was scrapped in 1891.
At http://www.greateasternsalvage.com there a is discussion of Great Eastern, and an appraisal of artifacts is available. Approximately one year ago I acquired an original photograph of her, which is displayed on the website (see "Links"). The ship was incredibly well built. With respect to her scrapping (which purportedly took some 18 months to accomplish), a body was discovered within the double hull. Every now and then on this board someone comes along and asks whether a body was somehow encased in the hull during Olympic's or some ship's construction - - perhaps this is where that story originates. Walter Lord's book, The Night Lives On, draws an interesting comparision between Great Eastern and Titanic.
Here's a photograph of the Great Eastern, from my collection. One of the funnels has been removed (to make space for cable) -- so the picture is from after 1862. Without any doubt, this is the "greatest ship" ever built.
There has been a curious transfer of legends from Great Eastern to Titanic. Walter Lord in ANTRII pointed out the "unsinkable" connection, but there is also the legend of the rivet basher who was allegedly built into the ship. In 1913 there were plenty of folk who had memories of Great Eastern, so this transferrence was probably natural. Both ships were launched with great expectations that never materialized.