The following has been the subject of some discussion on the GMF:
If an Owner or Moderator starts a "New Topic" then they can do so either as "themselves" or as the Group Owner. However, any replies they wish to make in any thread can only be done in their "personal" capacity.
1: Could things be changed to allow an Owner / Moderator to post replies (in any thread) as "Owner / Moderator".
However, when posting as an Owner / Moderator the individual's personal Display Name is shown on the website, and the email sent to members is sent as <Personal Display Name><Group Owner@...)
2: Could things be changed so that there is a separate Display Name for Owner / Moderator. Ideally this should be Owner selectable, perhaps with Owner / Moderator as a default setting, subject to the number of characters available in the Display Name field. (I don't think any limit is particularly low anyway, having looked at some of those on one Group!) The email sent to members should be <Owner><Group Owner@...) rather than the name of the individual.