"The Wandering Dago food truck wants to park and sell food at various events on New York State property. The state says no, because the name is offensive. Does that violate the First Amendment?" The answer is probably yes, says UCLA law professor Eugene Volokh at this link. He recently discussed the free-speech issue in a pending court case called Wandering Dago Inc. v. N.Y. State Office of General Services.
The mere fact that a business's name is politically incorrect, or offends some patrons, is not reason enough to ban it, as an appeals court ruled in holding the name "Sambo's" protected in Sambo's Restaurants Inc. v. City of Ann Arbor (1981). Of course, if it is offensive, the business may lose customers as a result, especially if its name does not appeal to patrons' sense of humor.
Commercial speech is not the only speech that government officials seek to restrict when it offends certain listeners. Such restrictions are common in universities, even though the Supreme Court has indicated that free speech is nearly as broad on campus as in society at large (in its decisions in Papish v. University of Missouri Curators, Healy v. James, and Rosenberger v. University of Virginia).
For example, Arizona State University has expelled a fraternity for a racially-offensive Martin Luther King Day party off campus. "Many condemned the students' actions at the Tau Kappa Epsilon fraternity party, which included partygoers wearing stereotypical hip-hop clothes and posing with hollowed-out watermelon cups, according to photos posted on the Internet."
While offensive, this expressive conduct appears to be protected by the First Amendment, under court rulings such as Iota Xi Chapter of Sigma Chi Fraternity v. George Mason University, 993 F.2d 386 (4th Cir. 1993) , which overturned a university's discipline of a fraternity for a racially and sexually offensive fraternity skit that the university claimed created a "hostile and distracting learning environment" for blacks and women.
As USA Today notes, "Gene Policinski, chief operating officer of the Newseum Institute in Washington, D.C.," which operates the First Amendment Center, stated that "the Constitution protects the students' right to dress in the manner they did as well as their offensive comments." Similarly, "Robert Shibley, senior vice president for the Foundation for Individual Rights in Education, said choosing a party theme is an expressive act, intended to communicate a message and is therefore protected by the Constitution."
Moreover, the fraternity's offensive expression did not appear to be aimed at minority students, much less any particular minority student, which undercuts any suggestion that the party was harassment not protected by the First Amendment. In 2010, the federal appeals court with jurisdiction over Arizona State quashed a racial harassment suit against a professor over his recurring racially-charged anti-immigration emails, citing the First Amendment and the fact that the emails were not targeted at any particular Hispanic complainant. (See Rodriguez v. Maricopa Community College, 605 F.3d 703 (9th Cir. 2010).
Moreover, if it occurred off campus, that also undermines any claim that the fraternity's expression was racial harassment in violation of the federal statute banning racial discrimination in education (Title VI), even assuming that Title VI could somehow supersede the First Amendment, which courts have indicted it does not. (See UWM Post, Inc. v. Board of Regents, 774 F. Supp. 1163, 1177 (E.D. Wis. 1991)). Courts have generally held that even serious misconduct off campus, such as assaults, do not create a hostile learning environment on campus, even when the assault was committed by an agent of the university, like a professor. (See, e.g., Lam v. Curators of University of Missouri, 122 F.3d 654 (8th Cir. 1997)).