The department I'm in recently changed it's name. However, in Sitecore, I have some groups whose name contains the old department name. I'm having trouble finding any way to rename these groups to use the new department name. There is no edit or rename option in the Role Manager.
Is there any way to rename a group after it has been created? Or is the only option to recreate that group, and All its permissions (quite the task)?
Sitecore stores permissions for items in clear text and they are not linked to the role with anything but the name so if you rename a role that you have used it on items then when you rename it authors will no longer have any right. If you haven't used the role then you can go and change it in the aspnet_Roles table as @Bryan advises.
There is one more way. You can create a new role and give it the name you want and add the original role to it. This way authors will get the same permissions but have the new role.