In file layouts/SlideOut/SlideOutLayout.js you can find layout controller code.
Here in the end of the method _createNavigation put your code adding logotype to slideout:
_createNavigation : function(navigationCommands) {
// existing code goes here
this.$slideOut.find(".dx-slideout-menu").prepend("<div class='logo'>My Logo Here</div>");
}
Of course you can put any markup you need. In my example the logo could be background of the div.logo.