The Hogwarts house-elf who loves butterbeer is Winky. She served the Crouch family and was especially devoted to Barty Crouch Sr. In Harry Potter and the Goblet of Fire, she is dismissed after being found at the site of the Quidditch World Cup while holding Lord Voldemort’s wand, although she insists that she was protecting her master’s son, Barty Crouch Jr.
After her dismissal, Winky is employed at Hogwarts, where Dumbledore gives her work alongside Dobby and other house-elves. She struggles badly with the loss of her former position and becomes dependent on butterbeer. The drink contains very little alcohol for humans, but it affects house-elves much more strongly; Winky’s consumption becomes a recurring sign of her distress.
Dobby is another Hogwarts-associated house-elf, but he is not the answer to this question. Hokey served Hepzibah Smith, while Kreacher belonged to the Black family. Winky’s butterbeer habit is specifically connected with the events following her dismissal by Crouch Sr.