You can modifying the name, description and accompanying image for your group at any time by using the 'Edit Settings' menu. This can be handy if you want to repurpose a group or point members to updated information via the associated weblink.
This can be undertaken by any group member with administrator priveleges.
Changing a member's status within a group
Each user's entry on the Members tab of your group will contain a dropdown menu which looks like a traditional user icon.
You can use this menu to modify a user's status and rights within your group - or to communicate directly with them via message.
Use the menu to 'Transfer group ownership' to a particular user, 'Make admin' to give them the ability to administrate the group (such as approving membership applications) or to 'Remove from group' if want to revoke access.
Closing a group
If you want to delete a group, you can simply right click on the group name in left-hand panel of Mendeley desktop and choose 'Remove group'.
If you are the only member of the group, you will simply be asked to confirm its deletion.
If the group has other members, you will be asked if you wish to transfer ownership to another member. Doing so will mean the group's storage is assigned to their account, rather than you - so may be an option in some cases.
Only the group owner can close a group.