Who is responsible for defining a site logo? I mean, there are moderators of the site that define it, or stackexchange defines it?
Our designers come up with the overall site design (including the logo), with some input from the communities. (With the exception of sites that are still in beta or have only recently graduated - those all share the same design.)
Community managers monitor per-site metas, so if/when the discussion concludes and the site's community largely supports a change, they can bring your concerns to the design team.
(And if by "logo" you mean "favicon", the process is largely the same - start on the site's meta and we'll go from there.)