"Shahs of Sunset" producers want to school an FHM model on the law -- telling her she has no right to sue over her handle "Persian Barbie" ... because Mattel trademarked the name a looong time ago!!

TMZ broke the story ... Persian model Niki Ghazian (above) accused the reality TV show of illegally using her self-proclaimed moniker, "Persian Barbie" ... for new cast member Lilly Ghalichi.

Now Berne Productions -- a subsidiary of Ryan Seacrest Prod. -- is responding to Niki's cease and desist letter with its own docs claiming she has no stake to the Barbie trademark.

Berne argues the term "Barbie" is 100% owned by Mattel -- and adds, "Any claim that Ms. Ghazian has acquired any property rights to a term that is a basic derivative of "Barbie" (i.e. "Persian Barbie") is unsound and not defensible." Aka ... go kick rocks, Ms. Ghazian.

Berne also claims 'Shahs' isn't violating Mattel's trademark because "Persian Barbie" is merely descriptive of Lilly's rockin' bod.

Exhibit A ...

There can only be one "PERSIAN BARBIE" ... so says a smokin' hot model who claims Bravo's show "Shahs of Sunset" is illegally using HER moniker for one of their cast members.

Niki Ghazian (left) -- FHM model and self-proclaimed "Persian Barbie" -- fired off a cease and desist letter last week to Bravo honchos ... claiming the network has no right to use the term for its newest star Lilly Ghalichi (right).

FYI -- Lilly's co-stars refer to her as the "Persian Barbie" on the show ... which Bravo has utilized in promos and on Lilly's official bio.

Niki says that's not okay -- and while she never applied for a trademark, she says she's the "common law owner" ... claiming ever since 2005, publications like FHM, Kandy Mag, NYLA Mag and more have used it to describe her.

Niki is demanding Bravo stop using the term ASAP -- and remove it from their ads, website and any other press releases ... or else.