How to display the name of file which I am currently editing with vim on terminal title?

You must to have/create a file named .vimrc in your home directory with the following code inside:

let &titlestring = $USER . "@" . hostname() . " " . expand("%:p")
if &term == "screen"
  set t_ts=^[k
  set t_fs=^[\
endif
if &term == "screen" || &term == "xterm"
  set title
endif

Source: gnome-terminal does not allow changing the title

The current (accepted) answer doesn't work if you switch files/buffers within one of your vim sessions. The title won't get updated.

The following is enough to have automatically updated titles in gnome-terminal also when you switch files by using :e foo.txt, :b0, :b#, etc.

Just place this in your ~/.vimrc file:

autocmd BufEnter * let &titlestring = ' ' . expand("%:t")             
set title

System: Ubuntu 14.10, vim 7.4.273, gnome-terminal 3.6.2-0ubunt.

Simply add

set title

to your ~/.vimrc.

Example title: testfile (~/Documents) - VIM