Can the group email address can be changed?

The @gaggle.email address you set when a group is created cannot be changed; it remains constant for the group's lifetime. You can change the group name in the Design area of your group dashboard at any time.

For paid groups, there are options to use your own custom domain. It can be set up and changed at any time. You can either use an email redirect or host your domain with us via an MX record.