The surname, Bleediotie, sounds phonetically like the phrase "bleedie outie", a bastardised form of the phrase "bleeding out", which is what would have happened had the surgery succeeded.
In an effort to capture Klaus and Sunny Baudelaire in addition to killing Violet, Count Olaf disguised the kidnapped girl as Laura V. Bleediotie and hid her in a hospital room before she was drugged into unconsciousness. Luckily, her siblings used their knowledge on anagrams to figure out her whereabouts and rushed to her rescue. Unfortunately, Olaf planned to decapitate Violet by forcing a reluctant Klaus (in disguise) to perform a cranioectomy.
The disguise was divulged after Klaus and Sunny managed to stall the operation long enough for Violet to regain consciousness, but at the cost of revealing their identities in front of the entire operating theater as well.
In the Netflix series, Violet still wears her original clothing under her hospital gown- being a pale yellow shirt and red overalls- and her hair is not pushed over her face, though her face is covered by a mask that administers sleeping gas.