Step 1
Log in to Facebook and Go to your Group.
Step 2
Click on the button in the upper right-hand corner of the page labeled "Edit Group" from the group page.
Step 3
Change the name listed in the "Group Name" field to rename the group.
Use the pull-down menu to select an icon to represent your group.
Changes can also be made to the privacy settings, email address and
description of the group. Click "Save Changes" when the edits are
complete.
Step 4
Click on the link in the upper right corner of the screen labeled "Back
to Group." Changes made to the group name immediately become visible.