Very good and relevant question as the Supreme Court recently decided to hear a case involving this issue. Here’s an article about it in the Washington Post. In short, an Asian American band called the Slants are appealing the USPTO’s refusal to allow that name to be registered as a trademark. An appeals court affirmed the USPTO’s rejection, stating that the First Amendment protects “even hurtful speech that harms members of oft-stigmatized communities.” This is getting a lot of attention because the decision could impact the use of the “Redskins” name & logo by the NFL team in Washington.
In terms of the rules provided by the USPTO, this is from a USPTO pdf on the Basic Facts of Trademark Registration:
“The USPTO will also refuse registration of a proposed mark for many other reasons, including but not limited to the mark being: a surname; geographically descriptive of the origin of the goods/ services; disparaging or offensive; a foreign term that translates to a descriptive or generic term; an individual’s name or likeness; the title of a single book and/or movie; and matter that is used in a purely ornamental manner. While some of these refusals are an absolute bar to registration, others may be overcome by evidence under certain circumstances. For more information about these and other possible refusals, see Chapter 1200 of the Trademark Manual of Examining Procedure (TMEP) athttp://tess2.uspto.gov/tmdb/tmep.”
So, it looks like there is a basis for rejecting a potentially offensive name. Hope this helped.