I was looking for this everywhere and I think I figured it out with a little bit of js. If you have your logo visible and linked to home on desktop, adding this script to header element in code injections worked for me. I'm using Brine.
<script src="https://ajax.googleapis.com/ajax/libs/jquery/3.2.1/jquery.min.js"></script>
<script>
Y.on('domready', function(){
var mobileLogo = Y.one(".Header-branding").cloneNode(true).addClass('mobile-logo');
Y.one(".Mobile-overlay-menu-main").prepend(mobileLogo);
});
</script>
I'm know very little js so if someone has a cleaner answer, I'm open to it. I just couldn't find a solution ANYWHERE so thought I would jump in. Hope it helps!!