Do I have recourse for being terminated for describing my last name?

Yes, you could be fired for this. All states are at-will states if you don't have a written employment contract protecting or guarantying your job; in an at-will state, an employee may be terminated at any time for any reason not specifically barred by law. And even when there is some specific legal protection, as there is for national origin (so you *might* be able to claim that your German name is protected as part of your national origin, though if you yourself or your parents are not Germany, the claim gets attenuated), the problem is that the employer must only make a reasonable accommodation for those factors and can terminate even otherwise protected employees for inappropriate behavior. And referring to yourself or your name as "male genitalia man" is unfortunately inappropriate: it would not only be offensive to many people, but could actually possibly be considered sexual harassment (e.g. making a male genitalia reference to female employees would almost always be considered sexual harassment--there is no time or circumstance, other than possibly in a urologist's office, when you can make a statement involving male genitalia to female colleagues). A company is not required to accept the risk of a sexual harassment claim and concommitment liability that your comments expose them to...especially since there are easy and fairly obvious non-genitalia-related ways to get the spelling of your name across, such as:
"That's Dickman: D-I-C-K-M-A-N.
"It's Dickman, not Rickman, as in Dick Tracey or Dick Nixon."
"That's almost right, but the first letter is 'D'."
That is, you could have conveyed the spelling without referring to genitalia. Since you used a frequently offensive, potentially sexually harassing way to describe your name instead of the several non-offensive options, your termination was legal.