The name 'Big Ben' apparently came about from the press at the time referring to the project as 'Big Ben'. It is said that term was popular for anything that was big as there was a famous professional fighter at the time called 'Benjamin Caunt' that weighed in at 108kgs, and fought some battle with another guy called 'Bendigo' and drew after 60 rounds.
The other interesting thing about it was the guy in charge of the project was a well known, pain in the arse, know-it-all and made the founders build the 13 and a half tonne bell to his own specifications. It cracked after a month of use. Rather than go to the trouble of building another 13 tonne bell, they rotated it and made the hammer smaller. It still has the crack in it which is why it sounds funny. Clearly a rare shot of the clock in that there are no clouds.