Home on the Range

Maggie is the only cow left on the Dixon Ranch after Alameda Slim (a cattle rustler capable of stealing 500 in a single night) stole all the rest of Mr. Dixon's cattle. Dixon sells Maggie to Pearl, a kind and elderly woman who runs a small farm called Patch of Heaven. The local Sheriff arrives to tell Pearl that her bank is cracking down on debtors. Pearl has three days to pay the bank $750, or her farm will be sold to the highest bidder. Hearing this, Maggie convinces the other cows on the farm (Grace, a happy-go-lucky character, and Mrs. Caloway, who has had leadership go to her head) to go to town to attempt winning prize money at a fair. While the cows are in town, a bounty hunter named Rico (who Buck, the Sheriff's horse, idolizes) drops a criminal off and collects the reward. Stating he needs a replacement horse to go after Alameda Slim while his own horse rests, he takes Buck. When Maggie find out that the reward for capturing Slim is exactly $750, she convinces the other cows to try to capture him to save Patch of Heaven.
That night, they hide among a large herd of steers, when Alameda Slim appears. Before any of them can do anything, Slim begins a yodeling song which sends all the cattle (except Grace, who is tone deaf) into a trance that causes them to dance madly and follow Slim anywhere. Grace is able to bring Maggie and Mrs. Caloway back to their senses just before Slim closes the path behind him with a rock-slide to stop Rico and his men from chasing him. As Rico discusses with his men what his next move will be, Buck starts talking with Maggie, Grace, and Mrs. Caloway as old friends and miming actions. This causes Rico to believe Buck is frightened by cows, so he sends Buck back to the Sheriff. Buck escapes, determined to capture Slim for himself to prove his worth.
Maggie, Grace, and Mrs. Caloway continue their search for Slim, determined to pass Buck and get to Slim first, but they have a fallout when they lose the trail in a downpour. Mrs. Caloway accuses Maggie of wanting to go after Slim only as a personal vendetta, arguing that she and Grace are better off without Maggie. The three spend the night under a large rock, with Maggie deciding to leave the next morning while Grace and Mrs. Caloway decide to return to Patch of Heaven to say their final farewells. The next morning, however, they are awakened by a peg-legged rabbit named Lucky Jack, who has also lost his home, an old mine, to Alameda Slim. Maggie decides to go after Slim with Lucky Jack in tow, but Grace convinces Mrs. Caloway that they help. Lucky Jack leads the three cows to Slim's hideout in Echo Mine. At the mine, Slim reveals that he has been stealing all cattle from his former patrons. When his former patrons can no longer support their land, Slim buys the land when it is auctioned off, under the guise of the respectable-looking Yancy O'Dell, using the very money he gets from selling the cattle he stole.
After arriving at Slim's hideout, the cows capture Slim. They run off with Slim's accomplices and buyer in pursuit on a steam train. Rico arrives. When the chase stops, Rico is revealed to work for Slim. Crushed by this, Buck decides to help the cows and fights Rico while setting the other cattle free. Slim dons his Yancy O'Dell costume and leaves the cows stranded in the middle of the desert with the train, while he goes to attend the auction. However, the cows arrive using the train to the farm and expose Slim. Slim is arrested, and Patch of Heaven is saved by the reward money.

Question: What's the name of the rabbit?
Answer: Lucky Jack