From the experts:
A relatively common surname, Dixon would be an inventive way to honor an ancestral Richard or Dick, the X form a lot livelier than the Dickson spelling, just as Dix is a more modern short form than Dick; it would be right at home alongside Dax and Jax.
But you don't need us to point out the considerable downside of this name. Besides being a sexual slang term, dick is also the most common epithet describing someone who's a jerk or a meanie (trying to avoid other unsavory words here). And Dix sounds exactly like dicks, which makes it not the least bit easier a name to carry these days than Dick.