Over the years I've seen several references and questions--basically, why THE Beaver? On FB someone had a pretty simple answer, which could be right:

The answer is (maybe), it's part of Theodore. Wally probably said something like, Twedor, which eventually became The Beaver.

I'll buy it!

I always liked ‘Beaver.’ I didn’t like when they referred to him as “The Beaver.”

As long as they do not call him "Happy Boy" like they do in some countries.

Never heard that one. You'd think there would be a translation for Beaver in all languages.

"And Jerry Mathers as the Happy Boy."

In the Italian version of the show they called him "Billy."

I seem to remember an episode where June explains the Wally could pronounce Theodore and hence Beaver was what it sounded like +-

Thee Door = Bea Ver +- ?

In the final episode they explain that Beaver got his nickname because Wally couldn't pronounce Theodore, so he turned it into Tweedor and this became Beaver.

Very lame explanation, in my view. It would have been more plausible to say that they called him Beaver simply because it rhymed with Cleaver, or because his front teeth resembled a Beaver's, or because he was busy like a Beaver.

In Beaver Gets 'Spelled, Miss Canfield asks Beaver if that's his given name, and he replies that his brother given it to him. So they could have explained that his baby teeth stuck out like a beaver, and Wally pointed at him and called him Beaver.