Once a folder is created in Content Browser, it’s impossible to rename it. Rename menu item in contextual menu is always disabled, and none of other usual tricks (double-clicking etc) seem to work.
I can confirm that right-clicking and choosing to rename folder is not working in Content Browser. -This has been reported as UE-30134 and is being tracked in following AnswerHub post:
[Cannot Rename Folders with Unreal Engine 4.11.2][1]
However, as a workaround, you can press F2 to rename folder or alternatively, you can change folder name in Content Viewer panel to right as shown here: