Your question should be 'Why don't you use 'the' in this question?' And the answer is simply that it's a name, or in fact, a nickname in this case. You don't say 'I want to see the Monica', so you don't say 'I want to see the Big Ben'. Some places have 'the' as part of their name, others don't. For example, the royal family's residence in London is called Buckingham Palace, without 'the'. It's not 'The Buckingham Palace', so you would say 'I want to see Buckingham Palace' - with no article. You might want to see Trafalgar Square in London. This is the name of a square, so there is no article. 'I want to see Trafalgar Square' - again there is no 'the'. By the way, 'Big Ben' isn't what people think it is. It isn't the clock or even the tower. 'Big Ben' is actually the name of one of the bells inside the tower.

We do not use "the" because "Big Ben" is a proper noun. It is the name of a place or thing. For example: I want to see Brigitte. (that's me!) We cannot say: I want to see THE Brigitte.

Generally you don't use the article "the" to help identify something or someone where the proper name for that person or thing is being used. But exceptions abound. You would say I want to visit the United States then in the next sentence say I want to visit Texas and both are correct. You might say"the" prior to identifying someone by a title ("I want to visit the Captian") and in the next sentence say "I what to see John". Not sure if that help's much or not.