This snippet (which should go into your emacs config file) will update your tmux window name with the title of the buffer you're currently in which is usually the filename of the file you're editing.

emacs-tmux-integration.el

(require 'deferred)
(defun rename-tmux-window()
  (deferred:$
    (deferred:process "tmux" "display-message" "-p" "'#I'")
    (deferred:nextc it
      (lambda (x)
        (setq x (replace-regexp-in-string "\'" ""
                 (replace-regexp-in-string "\n\\'" "" x)))
        (setq w
          (replace-regexp-in-string "\*" "" 
            (car (mapcar
              (function buffer-name)
                (buffer-list)))))
        (deferred:process "tmux" "rename-window" "-t" x w)))))

(add-hook 'change-major-mode-hook 'rename-tmux-window)