You can only change the name of a group you admin if it has fewer than 5,000 members. To change the name of your group:
Note :- All members of the group will receive a notification that the name has changed.
Note: We don’t allow admins to change a group’s name when the group reaches 5,000 members to prevent abuse. We do this because closed and public group names, members and group descriptions are visible to anyone and may be seen as part of someone's identity on Facebook.