Here's a handy function that I use to rename files in VIM (works in MacVIM and Neovim too)

function! RenameFile()
    let old_name = expand('%')
    let new_name = input('New file name: ', expand('%'), 'file')
    if new_name != '' && new_name != old_name
        exec ':saveas ' . new_name
        exec ':silent !rm ' . old_name
        redraw!
    endif
endfunction
nnoremap n :call RenameFile()

NOTE: I've used which is mapped to comma in my config. but you can use whatever key combiniation you like.