There are actually several VIVITs, namely Vivit (Erich's Daughter), VIVIT (Shuusou Gyoku's heroine), VIVIT-r (Banshiryuu's heroine), and many others (seen in Banshiryuu's 4B stage, as normal enemies).
VIVIT the robot maid was named after Erich's daughter.
"Vivit" means in latin "he/she/it lives".
VIVIT's attacks (mostly involving stars, with her signature move being a meteorite bombardment) and her tendency to carry a broom is remisincent of a certain witch.
VIVIT may have been referenced in the story in the Track 2 section of Dolls in Pseudo Paradise where Reimu quotes "Huh, that girl ... doesn't look like a human or a youkai".