Administrators of Facebook groups have the ability to change the name of the group.For Change the name of your facebook Group it is Compulsory that your Group members should be less then 250.
If the members are more then 250 then you have to Delete some members of your group.
Once the group name is changed, all members of the group receive notification. Correct spelling mistakes or make the group more identifiable by changing the name on Facebook.

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.