Sue Bird's TOGETHXR company has made good on its threats ... its now filed a lawsuit against The Rock's XFL over the league's rebranded logo less than a month after initially claiming it was way too similar to theirs.
The lawsuit, obtained by TMZ Sports, was filed on Wednesday -- nearly four weeks after Bird and her fiancée, Megan Rapinoe, threatened to get lawyers involved following the XFL's creation of a new "X" logo.
In the lawsuit, TOGETHXR -- a media org.