how to let tab display only file name rather than the full path in vim

Try

:set guitablabel=%t

For format of possible options see

:help 'statusline'

I use this solution instead of Habi's as this one still keeps the default features of putting a '+' symbol in the tab to indicate the files being modified, as well as a count of the number of windows in the tab. So it basically works the same as the default tab labelling but just uses file names, not full paths.

" Tab headings
function GuiTabLabel()
    let label = ''
    let bufnrlist = tabpagebuflist(v:lnum)

    " Add '+' if one of the buffers in the tab page is modified
    for bufnr in bufnrlist
        if getbufvar(bufnr, "&modified")
            let label = '+'
            break
        endif
    endfor

    " Append the number of windows in the tab page if more than one
    let wincount = tabpagewinnr(v:lnum, '$')
    if wincount > 1
        let label .= wincount
    endif
    if label != ''
        let label .= ' '
    endif

    " Append the buffer name (not full path)
    return label . "%t"
endfunction

set guitablabel=%!GuiTabLabel()

I have the following in my vimrc:

set guitablabel=\[%N\]\ %t\ %M 

which outputs: [Number] Filename and + sign if a file is modified ([4] foo.html +). Number is very useful to immediate switch to the chosen tab with command [Number]gt (4gt if I want to jump to the file in the tab 4)