The Battenberg - Mountbattens

[KikkiB]

I saw the film "Kate and Leopold" on tv this weekend, and got a bit of a shock. The male character, the Duke of Albany, Leopold (and he had a lot of other names as well) Mountbatten, had through a hole in the fabric of time as he put it, shifted from N.Y 1876 to contemporary N.Y.

So I reacted to the fact that this character had the last name of Mountbatten. Because Mountbatten is an anglification of the German Battenberg. And I know that the British Royal family had some names changing from German-sounding to English-sounding sometime in between the wars.

So my questions are, what is the history of the name Mountbatten? Is it likely that this character could have had this last name in 1876 in the USA? And what about the history of the family names of other royal families?