The story
19th-century invention, possibly from the Californian town La Verne, named in the belief that it means "the green" in French. Laverne is a genuine French surname, from Gaulish la verne "the alder (tree place)" but - as in the case of Leroy - there is no apparent reason to turn it into an American given name.
Etymology from Wiktionary, CC BY-SA 4.0.