Because Tadashi is somewhat of a "minor" character when compared to Hiro, Baymax and the team, a lot of times there isn't much info on him. But, lucky for you, 你 have Tadashi's #1 粉丝 here to find everything! These are just excerpts (so far theres only one ssshhhh), some may not be here because they are on video (which should be in the video section here!).
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 爱情 to pick at anything Tadashi-related, here is a small study thing I did a while back on 迪士尼 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 编辑 it).