Ward means warden and cleaver is something you use to chop things with.

https://thoughtcatalog.com/michael-leggs/2014/04/all-the-symbolism-you-never-knew-existed-in-leave-it-to-beaver-and-theres-a-lot-of-it/

Interesting article, but for a fan, he needs some corrections:

1. It's Larry Mondello, not Mundello.
2. Tooey is a friend of Wally's, not Beaver's.
3. Miss Canfield was only in season 1, not 2.