Go to 'My Groups' (by clicking your name in the top right of the page when logged in) and click on 'E-mail Addresses' under 'My Profile' on the right. From here you can add a new e-mail address, remove existing e-mail addresses and change which e-mail address is 'primary'.
To add a new address, simply type the e-mail address you want to add in the box under the ‘Add E-mail Address’ section. A verification link will then be sent to the e-mail address you just provided, so just click on the link in the e-mail to verify your ownership if this e-mail address. Once you enter your password again, your e-mail address will be added to your account.
To change your primary e-mail address, first add a new address, then make this new address primary by clicking the 'Make Primary' button. You can then delete your old (now non-primary) e-mail address if you want to, but be aware you will lose management access for any groups this address is a manager of, so you might want to add your new address to those groups first.
You can change the name from which your e-mails/newsletters go out by editing the 'From Name' in E-mail Template Settings.
Please note: The YourGroupName@groupspaces.com e-mail address can not be used as a personal address attached to a user account. These addresses are used for the e-mail discussion list feature only. If you add your group address to your user account you may accidentally spam your members with unwanted notification e-mails.