You can edit the 'From Name' on the 'Email Template' page to the name of your group, but the e-mail address will still be the manager's address, and replies will go to the manager.
To set a generic group address (if you have email@example.com for example) you can add it as one of the addresses attached to your user account:
- Click 'My Groups' from the drop down menu in the top right of the page that appears when you click your name
- Click 'E-mail Addresses' in the 'My Profile' section
- Add the firstname.lastname@example.org address in the 'New E-mail' box and then click 'Make Primary'
N.B. It is not possible to use your discussion list address (email@example.com) as the 'From' address. This is to stop unwanted replies going to all your members.