In order to rename a layer or layer group I have to double-click, pause, and then click again to be able to rename the layer in the layers palette.
Note: The double-click to rename a layer works correctly if you're using tabs for your documents, or if you are in "Full Screen Mode" or "Full Screen Mode with Menu Bar".
I can only reproduce this bug when using floating documents in "Standard Screen Mode", which is how I work.
Running:
iMac (27-inch, Late 2013)
Mac OS X 10.11.1 (El Capitan)
Photoshop 2015.1