Is there any configuration in PhpStorm that automatically renames file on remote host when you rename it locally and reverse?
There is no such option.
https://youtrack.jetbrains.com/issue/WI-19031 -- star/vote/comment to get notified on progress.
My only suggestion: enable automatic deployment option (as well as some others, possibly) -- it then should upload new file to remote and delete old file (no longer existing local file) from remote.