With this title being in Japanese, you might not think it's named after a jazz song... However, I actually found two possibilities.
The first is a 1953 track by Japanese jazz singer Miyoshi Umeki, titled "Sayonara (Let's Say Goodbye)". This was featured in the film "Seishun Jazz Musume", which was released that same year.
You can see the clip of her performance from that film here:
https://www.youtube.com/watch?v=pSqI0xZggU4
The second possibility is that it's named after the 1957 Nat King Cole song, "Sayonara". In which, at one point he literally says "Sayonara... Sayonara! Good bye..."
Have a listen:
https://www.youtube.com/watch?v=yf8M7UbGJyc