Let’s remember that the name Danny Zuko comes from the 1971 stage musical, and did not originate in the movie. The writer, Jim Jacobs, based the story on his experiences at Taft High School in Chicago and indeed the play was first produced in Chicago. There is a sizable Slavic population in Chicago and I’m sure Mr. Jacobs was familiar with shortened Slavic names where the “ski” or the “wicz” was dropped. Also remember that in the movie Sandy’s last name was Olsson but in the play it was Dombrowski and she wasn’t Australian!
I’d say that because of John Travolta’s popularity as Vinnie Barbarino and as Tony Manero, he naturally Brooklyn-Italianed it up for the movie, leading to the impression that since the name ends in a vowel it must be Italian.