You can use the function
bool ABRecordSetValue (ABRecordRef record,ABPropertyID property,CFTypeRef value,CFErrorRef *error);
record
is the reference to the group record in the address book
property
is the kABGroupNameProperty
property that represents the group name
value
is the new group name
Afterwards you have of course to save the address book with
OK = ABAddressBookSave(addressBookRef, &error);