I know this is a very old request, but I have just been looking around for a solution to this. Being able to rename files and directories in the file explorer panel by tapping the F2 key would be a good thing - even if a new "rename" command is added to Sublime and we have to manually setup a keymap for it.
I am a Windows user and am constantly clicking on the files in the left-hand pane and pressing F2 to rename it.
Bump. You should absolutely be able to rename files & folders with F2 in Sublime's file tree. F2 is built in functionality to Windows Explorer so I don't see the logic in ignoring such an easy to implement yet beneficial feature.
Customer support service by UserEcho