Once considered putting a picture of Biggie cheese from the back at the barnyard movie for the dedication of my book with a eulogy and everything. Sadly, when I called up nickelodeon they wheezed before asking me to hold and eventually told me no.
I also once considered putting a shitty picture of me crying my eyes out somewhere on my block cover as a joke. There are various means of using logos, memes, or well known characters on or in your book. Oh, you meant like a product brand logo. Welp, I'm not deleting any of what I already wrote so you can keep that.
Authors have a different type of logo. There are three logo's an author can have, 1. Their face or a caricature of their face(this is the rarest and is probably closest to what you're thinking. Usually, this is just a face in one way or another), 2. Their name(these are the one's who become the most famous like Stephen king, Brandon Sanderson, Akira toriyama, etc. this usually happens to authors who publish a lot of books and have readers from various genres), and 3. Their story(this is the most common as many people will read a story and they won't care about the author or their other works but will drop everything for new content for that story. Think Star wars, Harry Potter, bleach, etc. these are usually longer series or instant hit classics).
