In nearly four hours of arguments, several justices questioned aspects of laws adopted by Republican-dominated legislatures and signed by Republican governors in Florida and Texas.
A definitive ruling for Trump would largely end efforts in Colorado, Maine and elsewhere to prevent his name from appearing on the ballot.
The court will weigh the First Amendment right to free speech against federal trademark law, and experts are wary that speech could ultimately be chilled.
The two cases are the first of several controversies appearing before the high court in the coming months about free speech protections online.
The Supreme Court declined to hear a case requesting the reconsideration of the “actual malice” standard as applied to public officials in media defamation cases.
The Supreme Court agreed Friday to decide whether state laws that seek to regulate Facebook, TikTok, X and other social media platforms violate the Constitution.
The Supreme Court sided with a Colorado web designer June 30 who argued her freedom of expression was violated by the state’s anti-discrimination law requiring her to create marriage websites for same-sex couples.
The Supreme Court brought new clarity to the First Amendment standard that applies to “true threats” on June 27 in the case of a Colorado man who sent thousands of harassing messages to a musician, requiring prosecutors to prove that a defendant was reckless.