I do not use those notifications, but I thought name was already part of savegrp notification...

No, just says "savegroup completion" with no mention of the group name. If you're looking for a particular group it's a real pain.....

Are you talking about subject line of email or what is inside email?

Sorry, I wasn't very clear. Subject line.

I'm using the following filter:
__________________________
DAY_OF_MONTH=`date '+%d'`
cat > /tmp/$DAY_OF_MONTH.lgtoMail
RCPT=$1
SUBJECT=`head -1 /tmp/$DAY_OF_MONTH.lgtoMail`
/usr/ucb/mail -s "$SUBJECT" $RCPT < /tmp/$DAY_OF_MONTH.lgtoMail
__________________________

which gives e.g. this subject line:

"NetWorker savegroup: (notice) NDMP completed, total 1 client(s), 0 Hostname(s) Unresolved, 0 Failed, 1 Succeeded. "

Just save the above filter as executable script and update the action in the savegrp completion notification accordingly