Named not for its own two towers but for the nearby, pre-existing Tower of London. Tower Bridge was designed by Horace Jones, the City Architect, in collaboration with the engineer, John Wolfe Barry. 8 years to build. See the picture source website for more details and go visit - it's a great view. The London Historians went and reported back. Discovering London has some stunning Unseen Images of Tower Bridge Under Construction, and some mind-boggling Forgotten Images of Tower Bridge as it Might Have Been. (2024: both those links have died.)
The Bridge suffered little damage during WW2 which is surprising if it truly was the real target for all the V1 rockets, as some claim.