It is not. The nickname “Big Ben” technically refers to the bell in the clock tower – the tower itself is officially called the Elizabeth Tower, in honor of Queen Elizabeth II. The bell was installed in 1858 and was probably named after her Mr. Benjamin Halla civil engineer and Member of the House of Commons whose name is on the bell.
There is a less likely theory that the bell was named after Ben Caunt, a boxing champion who called himself “Big Ben”. While this theory is much more fun, it cannot be proven.