If you want to rename a folder in a SharePoint 2010 site programmatically, you can set the “Name” property of folder item. Please see the following code snippet for more information.
sourceFolderPath = "http://mysharepointsite/teams/documents/folder";
SPFolder lotFolder = SPContext.Current.Web.GetFolder(sourceFolder);
lotFolder.Item["Name"] = "<Specify New Name>";
lotFolder.Item.Update();