The story
Uncertain. Scooby doo appears as a vocable scatted in "The Boppenpoof Song" written in 1954, as the name of a band (The Scooby-Doo All-Stars) in 1956 and the title of a song by the Jerry Lieber Beat Band published by Zephyr Records in 1959 (both of which were signed to Zephyr Records), and lyrics in the song "Denise" by Randy & the Rainbows in 1963. It is likely that such uses were an influence on the creators of the cartoon but they may also have been partially influenced by Frank Sinatra's "doo-be-doo-be-doo" improvisation in "Strangers in the Night" released in 1966 a few years prior to the first episode of Scooby-Doo being shown (in 1969).
Etymology from Wiktionary, CC BY-SA 4.0.