Why is Bugs Bunny's first name "Bugs"?

There are several possible explanations:

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 Charlie Thorson describes this prototype character as "Bugs' 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. 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 1989, describes the "tough little stinker" that was the eventual version of the redesigned character as directed by Tex 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' Bunny".

A Wild Hare (July 27, 1940) was the debut of Bugs Bunny as we know him today. (...) The cartoon was so successful that WB decided to keep him on as a recurring character, eventually becoming the studio's most popular cartoon character. The character's name, previously only used on model sheets, became the official all-purpose name as well, with one modification: the apostrophe was dropped from his first name (now pronounced "bugs" rather than "bugs-es"). A title card saying "featuring Bugs Bunny" was slapped onto Elmer's Pet Rabbit after initial production of that cartoon wrapped up, though that cartoon had the rabbit carry the pre-Wild Hare characteristics.