How to automatically set iTerm2 tab title to the filename opened in vim?

I don't have iTerm, so I can't test this, but try adding this to your .vimrc:

set t_ts=^[]1;
set t_fs=^G

Type CTRL-V Escape for ^[ and CTRL-V CTRL-G for ^G.

This works for me:

" Set the title of the Terminal to the currently open file
function! SetTerminalTitle()
    let titleString = expand('%:t')
    if len(titleString) > 0
        let &titlestring = expand('%:t')
        " this is the format iTerm2 expects when setting the window title
        let args = "\033];".&titlestring."\007"
        let cmd = 'silent !echo -e "'.args.'"'
        execute cmd
        redraw!
    endif
endfunction

autocmd BufEnter * call SetTerminalTitle()

Source: https://gist.github.com/bignimbus/1da46a18416da4119778