FKA Twigs Told to 'Embrace New Name' By The Twigs Back in 2013, Alleged Emails Show

FKA Twigs was told early on by an indie band to leave the past behind and pick a new musical moniker ... according to emails the band says it sent back and forth with her in 2013. Here's the deal ... back in March, FKA sued the band The Twigs -- an…