"Alice" was the "name" of a girl that Jervis Tetch, aka Mad Hatter, abducted to fulfil his delusions of being the Alice in Wonderland character of the same name.
History
The girl was abducted by Jervis Tetch, a neuroscientist suffering from delusions of being the Alice in Wonderland character Mad Hatter (hence his criminal codename), sometime before Christmas Eve. During her time under the Mad Hatter, he managed to brainwash her, dress her in an outfit resembling the titular character from Alice in Wonderland, and gave her the name "Alice". On Christmas Eve, during an attempt by the Mad Hatter to contact the masked vigilante Batman shortly after the latter did his investigation of the Lacey Towers Murders, the girl interfered with the call and cried for Batman's help, but ended up silenced by the Mad Hatter, also citing that she's been through "a lot this evening." After Batman arrived at Tetch's office and ended up escaping his brainwashing measures, the girl was threatened by the Mad Hatter, who used her as a shield and placed a knife at her throat in an attempt to ward off the Dark Knight. However, Batman outsmarted the deranged neuroscientist by using a reverse batarang on him, releasing the girl from his grip and resulting in his being knocked out. Despite being saved as well as promised that the police will arrive to put her in protective custody and arrest Tetch, the girl, deeply traumatized by her forced stay by the Mad Hatter to the extent that she started uncontrollably sobbing, told her savior in a terrified tone that it won't be safe for her, ever.