it was originally built to keep people out of london
Wikipedia has a comprehensive article on the building - including its history. See related link.
It isn't. There are several towers within the Tower of London and the White Tower is just one of them, albeit the biggest.
Beefeaters
It was named after the architect's muse - Dao Thong, which tranlsates into English as Trellick apparently.
There is no King of London, the person in charge of London is called the Lord Mayor. The place where the Crown Jewels of England are displayed is called the Tower of London.
The Shard
because they were
the men are called Yeomen
Londinium. Romans arrived 43CE
The castle is officially named Her Majesty's Royal Palace and Fortress, but it is commonly known as The Tower of London. It is located on the north bank of the River Thames in London. The castle was first built in 1078, and it now has over two million visitors per year.
The Tower of London was begun in 1078 0n the orders of William 1 on a site which originally was a Roman fortification, so is of international architectural and historical interest.