Bugs Bunny is a cartoon rabbit created by Warner Bros. His catchphrase "What's Up, Doc?" uses "Doc" in the same way Marty uses when he addresses Emmett Brown as Doc.
On October 2, 1982, after Emmett Brown had previously met Marty on his trip to 1955, but before Marty met him, he told Marty to call him Doc, knowing that Marty used that name when he met him in 1955. He explained that he wanted Marty to call him Doc, as in "What's Up, Doc?".
On March 3, 1986, Doc arrived in his second lab from 2035 after receiving a note from Marty. However, while in 2035, he received an electric shock from Griff Tannen and suffered amnesia as a result. He didn't realize that Marty was addressing him as Doc, thinking he was just talking like Bugs Bunny.