Kim Kardashian’s Skims brand is being sued by a small New York designer over the shapewear label’s use of the “Fits Everybody” name.

In documents obtained by Page Six on Friday, the “Kardashians” star’s fashion empire is being targeted over their Fits Everybody collection , with much smaller apparel brand Fits Everybody To A T claiming it already has rights to the name.

In the 43-page trademark infringement lawsuit — which was filed on March 31 in the Southern District of New York on behalf of Denise Cesare — Fits Everybody To A T claims Skims went ahead with launching its Fits Everybody collection even “after receiving repeated, unequivocal notice” of their rights.

It also alleges that Kardashian’s wildly popular lingerie brand identified “a trademark owned by a small, self-funded woman-owned business” and recognized that “the small business owner would likely lack the resources to fight back.”

Cesare is seeking an order barring Skims from continuing use of the name, as well as damages including legal…