You are able to change your Groups delivery settings from Groups menu.

1. Log in to your Google account and open Groups from application menu. 

2. Select My Groups

3. Open the group by clicking the name. 

3. From right upper corner, click My Settings and select Membership and email settings.

4. This will open a settings window. From here you can select message delivery settings and your display name.

5. Select the wanted delivery setting and click Save.