John,
... a moderator asked me if there is any way that a group member can
hide his email address but not his name when posting?
There is not.
While their email addresses won't be shown on the Groups.io site, their address will be in the From: address of their postings when forwarded to members that receive group messages by email.
The best the member can do is create or use an anonymous email address for use in the group.
That is, go to a free email service (aol, gmail, hotmail, etc.) and create an email address that does not identify them. They can put a filter in the anonymous account to forward to their preferred email address, but this is still inconvenient because it means that they always have to sign in to that anonymous email, or to groups.io, to post or reply.
I believe I can make the member directory only visible to owners &
Moderators ...
Correct.
There was considerable discussion, some time ago, in the beta@ group about having anonymous groups - where no member's address would be seen or forwarded to any other member (only moderators would see them in the Members list).
The idea was controversial and hasn't been acted on. I haven't seen anything about them this year. It is on the to-do list though:
Shal
Shal Farley