Some-role at FANG sounds more impressive than same-role at a no-name startup.
Even the startups themselves like to brag that they were started by alumni of brand name employers, rather than alumni of other startups.
So, in what concrete way can you shift this?
There is no easy solution, but you can try and follow the same route you did for startups.
No-name (YC 18) is a better brand then just-no-name.
Allow/encourage employees and encourage/require your startups to brand people as “YC Startup Engineer” rather than “no-name Engineer”.
It may sound a little strange at first but there is a probability bigger than zero that if you promote this correctly, as you did for startups, you may end up at top of the prestige pile.
Just 2 cents from a guy with none ;)