What amazes me is that people's "Buddhist" names all seem to be Asian. :-)
People 'get' their name from a guru, which is a form of initiation into that particular tradition, and so the new name is almost always related to the root culture from which that tradition sprung. The new name is a psychological device to provide a sense of belonging to that tradition, and pride is encouraged around it, since you have to meet approval to receive it.
There is really no reason your "buddhist name" needs to be from a particular culture. unless it is useful to you as a tool to walk The Path. If you need that sense of belonging, then its a wonderful thing.
But "naming" isn't a "Buddhist" thing. It is a traditional cultural thing that was brought along for the ride as a useful tool.