Sweeper being the nicknamer she is does have a few for her kin - since she perfers short or cutesy sounding names. Rain for Torrential Waters, Ami for Armifera Imperatrix, Wavy for Crashing Wave, and Arc for Arcon. Thea doesn't get one because her name already sounds cute to Sweeper. 

Of course, her kin may or may not like the friendly names Sweeper gives to her kin.