FKA Twigs says she's over being targeted by a band with a similar name ... so she's turning the tables by asking a judge to tell them to stop trying to take her to court over it.

According to a lawsuit obtained by TMZ ... FKA Twigs -- real name Tahliah Debrett Barnett -- wants a declaration from the judge to put an end to the indie twin-sister group The Twigs sending her cease-and-desist letters over their similar names.

Basically, FKA claims the sister act -- composed of Laura and Linda Good -- has been hounding her over the trademark to her name ... after she says they filed a trademark claim against her in 2014, before "voluntarily" dismissing the case and disappearing for a while.

After more than a decade passed ... The Twigs allegedly started up again -- sending cease-and-desist letters demanding FKA stop registering the trademark for FKA Twigs ... which they say infringed on their marks and caused confusion.

But FKA insists there's no danger of people mixing them up, saying it's "inconceivable that any member of the relevant consuming public could confuse Barnett’s offerings with those of Defendants or believe that the parties are affiliated or related to each other."

Bottom line -- FKA says she has had enough ... and is hoping a judge formally declares FKA can register her own trademark and puts an end to The Twigs' "attempts to weaponize" these old arguments about their similar names.