It is Italian/Spanish name.

It's a no way related to the Banda Islands which real name is "Bamda"

The King Bahdu or African King Banda is a mere Anglicanization of the name. The Banda people is also an anglicanization, their real name is bahmeda. It's very difficult to trace a surname with little or no roots.

The name appears to be rare, perhaps because the people who immigrated to Mexico/Cuba were sporadic. It is possible that it is an occuptional surname as well, which would explain incosistencies in relations.

You must understand that people change their names, quite frequently, for example, a Smith family of Germany may not be related to Smith from England, that's probably because someone changed their name.

I have a great grandmother who's name was Angela di Banda (Northern Italy only child of Salvadore Banda and Angela Ferritti Banda), she was Italian and she married my great grandfather a German immigrant. Remember this when searching for a surname, it doesn't always relate to other names, in fact your name could have been Bindy, Banhu, Banta, Bantu, and so forth.