Why does Dick Laurent have two names? The reason, according to an in-depth analysis posted at the blog 'I Talk You Bored', is not what's typically assumed: that "Mr. Eddy" is a pseudonym that Laurent uses for his dealings in the, ahem, erotic cinema business. In fact, there's good evidence to believe that Laurent is probably not involved in any such shady dealings at all.

The short answer is that "Mr. Eddy" is merely how Dick Laurent appears in the self-serving fantasy of Fred Madison, just as "Alice" is merely Fred's re-imagined version of his wife, Renee. Dick Laurent is the man Fred kills for sleeping with Renee (before killing Renee herself) and, in order to justify this murder to himself, his unconscious imagines Laurent as Mr. Eddy, a violent, sleazy hustler who "had it coming", so to speak.

For a longer version that explores Lost Highway in greater detail, check out the post: https://italkyoubored.wordpress.com/2013/01/30/david-lynchs-lost-highway-who-is-dick-laurent/