"Alice" was the "name" of a girl that Jervis Tetch, aka The Mad Hatter, had abducted to fulfill his delusions of being the Alice in Wonderland character of the same name.
That girl was abducted by Jervis Tetch, a neuroscientist who suffered from delusions of being the Alice in Wonderland character The Mad Hatter (hence his criminal codename), sometime before Christmas Eve. During her time under the Mad Hatter, he brainwashed her, dressed her in an outfit that resembled 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, who also cited that she had been through "a lot this evening." After Batman arrived at Tetch's Hat Shop and escaped 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 Batman. However, Batman outsmarted the Hatter by using a Reverse Batarang on him, which released the girl from his grip and resulted in him knocked out. Despite being saved as well as promised that the GCPD would 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 Batman in a terrified tone that it wouldn't be safe for her, ever. Alice was later taken care by the Police and was asked some questions about her kidnapping.