“If the French can protect ‘Champagne’, the Portuguese ‘Port’, the Spanish ‘Sherry’ and the Greeks ‘Feta’,” said Nick Xenophon, an Australian senator, in a recent statement, alluding to the brand protections that some famous names enjoy, “then surely Australia can protect the word ‘Ugg.’” (Mr. Xenophon on Friday said he would resign as a senator.)

Uggs came and went from public view in the United States since they were trademarked there, but they won a big boost from Ms. Winfrey, the talk show host, who came out as a fan in the early 2000s. Their roots are more humble. According to Australian trademark officials, they appeared as early as the 1970s in phone directory ads as ug, ugg, ugh boots, among many other variations.

“In Australian slang, ‘ughs’ are sheepskin booties, designed by surfers in the 1960s to coddle feet weary after ‘shooting the curl.’” The New York Times said in 1994.

The brand’s owner in the United States, the Deckers Outdoor Corporation, argues that in the 1990s it bought the American registered name from an Australian entrepreneur, Brian Smith, fair and square. Australians violate the company’s intellectual property rights, it said, when they sell Ugg-like footwear in the United States.

Last year it sued an Australian shoemaker owned by Eddie Oygur in a Chicago federal court, saying he sold ersatz Uggs in the United States. Mr. Oygur sold about $2,000 worth of lowercase ugg boots in the United States over a five-year period, his lawyer said, and believed he had every right to.

“I want to let the American people know what corporate bullies they are and what they’re trying to do – deplete my resources, ruin my business and the whole ugg boot industry,” Mr. Oygur said in his factory in Lidcombe, a Sydney suburb.