There are many obelisks around the world, especially in Egypt.  There are two obelisks named Cleopatra's Needle, with one in Central Park in NY City and the other in London.  

The obelisk in Stanley Kubrick’s 2001 has inspired decades of fan debate. What was it? Who put it there? What was its function?

It is a good example of how leaving a little mystery behind makes a story memorable.