Does my Anthropology PhD topic have to be the same as my Masters topic?
There is no such requirement unless imposed by some advisor that you might carry through with from the masters to the doctorate. But even then it is not essential in concept. 

You are free to explore new directions, and it is probably a good idea to do so. Assuming the common case in which you have a different advisor, or even if you are at a different university, take some (maybe a lot) direction from your new advisor. If you have your own ideas, explore them with the advisor. If you are more tentative, the typical case, look for suggestions from them about directions you might pursue. Perhaps the ideas will be in line with the general research trajectory of the advisor in such situations. 

And this isn't true just in anthropology. 

It is also important that if you are going to do serious research in some topic, that you have some affinity for that - it needn't be love exactly, but it is better if you are driven internally by the questions, rather than just following a script. 



Danger. Danger. Don't over stress my words just above. Be in love with the topic. But don't be driven to preconceived notions that you want to be true. Research is a search for truth. Be in love with the search, whatever emerges as the truth.