We want it to be very clear that Beta is indeed Beta and not just another world that gets updated earlier. Beta may be buggy and may even have features that will not be available for weeks on any other server (like a while ago when we launched Fellowships on Beta three weeks before they went to all the other servers). We want everyone to know that we are not the same as all the other versions. Having "Beta 1" as the name of the server helps us differentiate our Beta version from all the Live versions, which is exactly what we want.
Beta's first and foremost purpose is testing the game, reporting the problems as soon and as accurately as we can, in order to prevent issues going from Beta to the normal worlds (Live worlds). Live, on the other hand, is focussed (pretty much solely) on providing as many players as possible with the best possible gaming experience. Of course that is important on Beta as well, but our way of achieving that is by preventing problems from ever reaching the Live servers by making sure that issues get reported in time, while that is not the route that Live takes.
In short: Beta and Live servers are vastly different. Beta is about testing and having a good time while doing so, Live is about playing and having a good time in general. Having another name for our Beta world helps us differentiate between the two, which is why we won't change the world's name.
