I suggest the Notice that is sent to other Groups say:
[x Group's Admin] has changed [Member name and email address] from [email address] to [email address]
or
[another Group's Admin] has changed [Member name and email address] from [email address] to [email address]
instead of
[My name & email address] had changed [Member name and email address] from [email address] to [email address] in group [their group name].
If the "Member name" is not the name connected to the email address (with their Email Provider),
rather than their Display name (which can differ from Group to Group),
then [Member name and email address]
should just be:
[email address]
-Michael
Michael Pavan