Historically there is a difference between a name and a mere "word". Even if there is a Chinese word meaning "brother" that is pronounced "
Dee", that doesn't necessarily mean that there has ever been anyone in
China who has been given
Dee as a name with that being the intended meaning.
Every reasonably short word will probably have several different meanings in various languages around the world. But most of these will be accidental correspondences. Etymology is just not finding accidental similarities in sound, but is the study of where the name comes from historically. So it doesn't matter what "
Dee" means or meant in Hebrew or Chinese if there is no evidence that the origin of
Dee as a given name in English-speaking countries historically goes back to the Hebrew or Chinese words.
As a surname in Britain,
Dee is taken from Welsh
dhu, "black". That's a more likely derivation for your grandfather's middle name (if you have British ancestry) than a Chinese word.