Taylor Swift is officially laying claim to a nickname for a new part of her "Eras" tour -- and while it remains to be seen if it'll amount to anything ... she's at least locking down the rights.

The singer filed a trademark application last week -- and it touches on something she shouted out this weekend during her Paris stint ... namely, 'Female Rage: The Musical.'

In documents obtained by TMZ ... TAS Rights Management -- a company owned by Taylor -- filed paperwork to trademark the phrase ... which, as the singer explained on social media Sunday, was the theme of her newly added "Tortured Poets Department" set.

While the filing didn't indicate Taylor's plans for the trademark ... it does lay out everything she wants the right to do with the term, including turning into musical recordings, video recordings as well as slapping it onto a bunch of crap for potential merchandise.

The move might be protective ... as some fans have already started to try branding their own stuff with 'Female Rage: The Musical' -- so this could be Taylor blocking the vultures.

A number of shirts and sweatshirts have already popped up on Etsy, featuring the now viral saying and Taylor's likeness from her tour. So, it only makes sense for Taylor to try and monetize on the phrase ... or at the very least, protect her ability to make money off it.

Remember ... Taylor shook things up big time for the European leg of her Eras tour -- introducing at her Paris shows a new intro, a slew of costume changes, and several tweaks to the lineup.

Not only did Taylor rearrange the order in which she performed her different eras, but she also added 7 songs from her record-breaking new album, 'TTPD.'