rejeep-projectile-completion-fn.el

(defun rejeep-projectile-completion-fn (prompt choises)
  "Projectile completion function that only shows file name.
 
If two files have same name, new completion appears to select between
them. These include the path relative to the project root."
  (interactive)
  (let* ((stripped-choises
          (-uniq (--map (file-name-nondirectory it) choises)))
         (choise
          (ido-completing-read prompt stripped-choises))
         (matching-files
          (-filter
           (lambda (file)
             (equal (file-name-nondirectory file) choise))
           choises)))
    (if (> (length matching-files) 1)
        (ido-completing-read prompt matching-files)
      (car matching-files))))

(setq projectile-completion-system 'rejeep-projectile-completion-fn)