Obviously, it's always pretty likely that they chose his name simply because it's nice. But because I'm an obnoxious brat and I love to pick at anything Tadashi-related, here is a small study thing I did a while back on Disney Wiki.
These are the possible spellings of his name and the meanings of the different spellings (I don't yet know which meaning gpes to which spelling, when I do I will edit it).
Hamada, Tadashi (はまだ ただし):
Hamada can also mean "seashore rice paddy", which is weird, but kind of pretty to picture, ahaha.
Tadashi can mean: loyal, true, righteous, morally correct.
Tadashi can also mean something like "happy history" (tada, 'happiness' and shi, 'history').
All sorts of beautiful things come from his name, haha. He really is a good dude.