We can argue back on forth on what the implications of the names showing up are and aren't[1], but neither the referrers nor the referrals knew that this would happen. That's bad privacy on Uber's and Dropbox's part.
[1]: Not everyone manages to get people to sign up as fast as you did. The implication of this is that if I know who signs up and when, I can surmise their name based on this information, which violates the user's privacy. Again, privacy is very contingent on the implications of what a malefactor might be capable of.
Whether a mountain or a molehill, this is something that just doesn't serve any good purpose but comes with some negative consequences.
It's really none of my business who they are and would be an invasion of their privacy for me to know - in my opinion.
I guess an argument could be made for refer-a-friend programs working differently, but the default should always be sharing this kind of data only on a need-to-know basis.
I don't know if they could see my e-mail address as well, but it was extremely uncomfortable from a privacy perspective, so I ended up asking Dropbox if they would cancel my referrals.
Not that I don't want the storage, but it makes me uncomfortable that people I don't know might have my e-mail address, especially if I post the links in a context I believe to be anonymous or pseudonymous.