Actually (to be an absolute pedant!), it was never the 'Palace of Westminster tower'. Prior to 2012 when the name was changed (much to my chagrin) to the 'Elizabeth tower', it was 'St Stephen's tower'...which was a really good quiz question!
To be even more pedantic, it's none of those things. It's a series of black squares arranged to look like a pencil or a rocket ship or perhaps a bell tower in London of uncertain nameage (not a word but I don't know a better one).
it is in fact the "Palace of Westminster tower" or, since 1012, "Elizabeth Tower". Big Ben is the bell inside the tower.
Nice image of the iconic tower in any case.