I haven't used "Dory" but am assuming that yes, questions could be read without referring to their author. I interpreted from the OP's wording that screenshots/snapshots of Dory were leaked, and these leaks would have contained names attached to questions. The Google CEO doesn't elaborate, but maybe the Googlers who expressed concerns to him were afraid that when the questions were made public, doxxers would make public the identities of the questioners?

So sure, maybe the internal Dory system should have been configured for anonymity. Come to think of it, Google should have just used its own Forms, which allows respondents to authenticate via email address, and for responses to be stored into a private, management-only spreadsheet. I think it's safe to say Google has handled many aspects of its response to Damore in a sub-optimal way.

Few thing spook executives more than having to answer anonymous questions in front of the whole company!