The character that would evolve into Bugs Bunny appeared in four cartoon shorts before his first official appearance in Tex Avery's A Wild Hare. While this early version is commonly referred to as "Happy Rabbit", animation historian David Gerstein disputes this, saying that the only usage of the term was from Mel Blanc himself; the name "Bugs's Bunny" was used as early as April 1938, from a model sheet made by Charles Thorson which was used for the short Hare-um Scare-um. Bugs was also mentioned by name from an August 1939 review of the short in the Motion Picture Herald.

Several published first person accounts, encyclopedic references, and Warner Bros.' own published material describe the inception of the name and of the character. A model sheet by Thorson describes this prototype character as "Bugs's Bunny" (note the apostrophe) but in most of the cartoons the character is unnamed.

Virgil Ross, the animator for A Wild Hare describes how the character came to be named in the interview published by Animato! magazine #19. Mel Blanc often told the story of the creation of the character and its name. He suggested that the character be named after the character's initial director, Ben "Bugs" Hardaway. Blanc's own book, That's Not All Folks published by Warner Books in 1988, describes the "tough little stinker" that was the eventual version of the redesigned character as directed by Avery.

Warner Brothers' own published descriptions of the creation of the character's name can be found in Animation Magazine published in 1990. Therein it is described that the Hardaway unit's model sheet came to be known by fellow animators as "Bugs's Bunny".

Ben Hardaway and Cal Dalton introduced the first version of the character in Porky's Hare Hunt (released April 30, 1938). In the cartoon Porky Pig is hunting and fires at several rabbits. Soon, Porky and his dog meet the rabbit and try to outwit him in the forest. Porky and the rabbit get in a long fight and soon the hare thinks he has won and that the war is over; Porky, however, finds the rabbit and the Bunny doesn't have any brainstorms to protect him. The rabbit shows Porky a photo of himself and of how many children he has with his wife. However, when Porky's about to shoot him, the gun fails.

After Porky attempts to shoot down and procure the rabbit, the rabbit asks Porky: "Do you have a hunting license?" As Porky reaches for his pocket to obtain the document, the hyperactive hare suddenly snatches it out of Porky's grasp, rips it in two, remarks, "Well you haven't got one now...hoohoohoohoohahahahah..hoo hoo hoo ha ha ha!" and makes a getaway by twisting his ears as though they were a helicopter propeller, flying away. Ultimately the rabbit wins when Porky throws dynamite into the cave in which the hare is hiding and the rabbit throws the dynamite back at him. Porky is in the hospital and the rabbit comes to him with some flowers. Porky tells the hare that he'll be out in a few days. The very hyper rabbit then pulls on the leg holders in Porky's bed, adding to his injuries, and runs off into the forest.

Chuck Jones later directed the cartoon Prest-O Change-O (released March 25, 1939) that featured the rabbit. In this cartoon two rogue dogs are being pursued by a dog catcher until they hide in an abandoned house. There they encounter a trunk owned by Sham-Fu the magician (unseen). They open it, and all manner of magic tricks come out of the trunk, including his pet rabbit. The rabbit tricks the two dogs repeatedly, causing them endless frustration, until he is bested by the bigger of the two dogs, who bops him with a lampshade.

Schlesinger assigned Hardaway and Dalton to direct the next short, Hare-um Scare-um (released August 12, 1939). It starts with a man reading a newspaper article stating that meat prices have soared (and that customers are sore). Angry, he declares that he will hunt his own meat to get back at the government for the price inflation. He then tells his dog he is going hunting for rabbits.