One of the complaints I have seen about the new design is that it is more uniform that it used be and often it is difficult to distinguish sites from another.1 (Especially if you are viewing a question and scroll down.)
Proposal: Instead of Stack Exchange logo in the top-bar on the left, use a logo of the site.
This would add at least one more element which can help to distinguish various sites. Moreover, top bar stays there even if you scroll down.
When I tried to switch to mobile web, I saw that in mobile web site's name is already displayed in that place. Although in mobile web the top bar disappears when you scroll down (unlike in desktop version).
1I will admit that the only discussion related to redesign that I followed really closely was on MathOverflow (see: How can we visually differentiate MathOverflow from MathStackExchange within the constraints of the new design themes?) But it would not be a surprise if the same problem appeared on other sites. (Similarly as MathOverflow and Mathematics, this is more of a problem if there are two sites with rather similar or overlapping scopes.)