The 76-year-old rocker passed away at his home in England on July 22, just weeks after his final Black Sabbath gig.
He filed documents to trademark his nickname on June 13.
According to The Sun newspaper, his UK-based firm Monowise sent the application to the United States Patent and Trademark Office for "entertainment services, namely providing non-downloadable pre-recorded music via a website".
The company also sought trademark protection to sell clothes, games and accessories.
A ruling has yet to be made, although a similar claim was passed previously in the UK.
Meanwhile, it has been revealed that tributes left for Ozzy in his home city of Birmingham are to be taken down and given to his family.
Fans had flocked to the city to pay their respects to Ozzy as flowers, keepsake items and handwritten notes were left at Black Sabbath Bridge - a spot that marks the Paranoid band's formation.
The council said that the tributes will be preserved at a secure location before being passed on to Ozzy's loved ones.
Ozzy's family viewed the tributes during his funeral procession in the city and said they were "deeply moved" by the affection the public had for the Prince of Darkness - who had played his final gig with Black Sabbath at Birmingham's Villa Park stadium just 17 days prior to his death.
A statement read: "We are deeply moved by the heartfelt tributes that have been placed at the Black Sabbath Bridge and at the Black Sabbath mural on Navigation Street in recent days.
"These expressions of remembrance reflect the profound impact that Ozzy had on the city and its people, as well as fans from around the world - BIRMINGHAM FOREVER!"
Lord Mayor of Birmingham Zafar Iqbal said: "We understand how important it is for the community to have a space to grieve and celebrate Ozzy's legacy.
"We know fans will continue to pay their respects at the Black Sabbath Bridge and the mural on Navigation Street, as well as visiting the Ozzy exhibition."
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