ABC News' Felicia Patinkin reports:

The company that bought the rights to Princess Marcella Borghese's cosmetics line in the 1990s is suing members of the famous Borghese family, and central to the lawsuit is the question of who can claim the Borghese family history.

Prince Lorenzo Borghese, who appeared on season nine of ABC's "The Bachelor," and his family are being sued by Borghese Inc., the corporation that bought his grandmother's cosmetics line from Revlon in 1992. The company is arguing it owns the rights to sell products under the Borghese name and the right to use the Borghese family heritage to market those products.

While the Borghese family no longer has any part in the global company, it is still in the cosmetic business and does not use the Borghese name on any of its cosmetic products.

However, in 2010, the company, now run by Texas socialite Georgette Mosbacher and owned by members of the Saudi Royal family, filed a lawsuit against several Borghese family members, including Lorenzo Borghese - claiming the family's marketing strategy plays up the Borghese family heritage to sell its products.

The former "Bachelor" contestant tried to introduce a brand of pet products called Prince Lorenzo Borghese's La Dolce Vita. He claims to have the right to use the Borghese name because Borghese Inc. does not make pet products.

"Everything was fine until 2008 when I filed a trademark and they opposed it," Lorenzo Borghese told ABC News, referring to his pet products line.

"I don't use the same fonts. I'm in different retail outlets. Unless they're selling Borghese mud at Petsmart or Petco for dogs, I don't get it," Lorenzo Borghese said.

In a statement to ABC News, the Borghese company said in part: "The law concerning trademarks is clear and the precedents long-standing … Once a business obtains a trademark and invests in a business built on that trademark, U.S. law protects that brand, that investment and that business from trademark infringement and unfair competition."

Scroll down to read the full statement from Borghese Inc.

Both the family and the company claim each is being bullied and intimidated by the other.

The family claims the lawsuit-which it says has cost them $4 million in legal fees-has cost them emotionally, too

"I think my father feels that his family's being attacked … he wants to make sure that, you know, he can retire in peace and know that his family can use their name and share their history," Lorenzo Borghese said.

The family continues to fight the company that shares its name. Borghese says he's not just fighting for his family.

"I want to make sure that other companies, smaller companies, are no longer bullied and forced to sign away their trademark rights because they can't afford to… pay for their legal bills anymore," he said.

Full statement from Borghese Inc.

We at Borghese, Inc. take tremendous pride in our company and our brand - and do everything we can to ensure our customers are able to receive the authentic, high-quality Borghese products they love. You may recently have seen our company in the news or in some social media posts regarding our efforts to protect the Borghese brand legally against trademark violations and other types of unfair competition. We currently have a lawsuit pending against Home Shopping Network, Borghese family members and other corporations. Borghese family members have collectively been paid millions of dollars for the rights they sold and - in fact - continue to receive royalties today. They have had absolutely nothing to do with the development of the Borghese brand for more than 40 years and are not part of the company. We believe they have started the negative media and social media campaign in an effort to try to bully and intimidate us into compromising on the integrity of our brand.

The law concerning trademarks is clear and the precedents long-standing. Several well-known family names have been trademarked for product use - such as Gucci and Ferragamo. Once a business obtains a trademark and invests in a business built on that trademark, U.S. law protects that brand, that investment and that business from trademark infringement and unfair competition. The Home Shopping Network is well-aware of this and yet continues to violate the trademark rights of the Borghese company.

Rest assured, we are doing everything we can to ensure that authentic Borghese products remain in the market and that our loyal customers are not confused in any way. Thank you for support.

Editor's Note: Since publishing this story, Lorenzo Borghese has asked that we add this statement from him:

"As the founder and face of the Borghese cosmetic's brand, my grandmother was paid a salary until one year after her death. Once she died, her additional one year salary, according to her will, was split between my father and uncle. Since 2003, they have both been collectively paid less than $50,000."