Does anyone know the name of this song...?

Manamana is the name of the song - there are no actual words.... it was actually done by the muppets character Dr. Teeth (who was kind of a caracature of a real New Orleans singer Dr. John) and was voiced by the incomparable Jim Henson.

The original song is by Piere Umiliani and was called Mah Nà Mah Nà

It's a cute little nonsense song...

"Mah Nà Mah Nà" is a well-known pop music song, written by Piero Umiliani. It was a hit in many countries, including the USA, in 1968–1969. The song's lyrics contain no actual words, only nonsense words resembling scat singing. The original version interpolates melodies from "Swedish Rhapsody" ("Midsommarvaka" ("Midsummer Vigil")) by Hugo Alfvén, "Santa Lucia", "Boogie Woogie Bugle Boy", the jazz standard "Lullaby of Birdland", and others.

"Mah Nà Mah Nà" debuted as part of Umiliani's soundtrack for the Italian softcore pornography movie Svezia, Inferno e Paradiso (Sweden, Heaven and Hell) (1968), a pseudo-documentary film about wild sexual activity and other behavior in Sweden ("Mah Nà Mah Nà" accompanied a scene set in a sauna). A soundtrack album, "Svezia, Inferno e Paradiso" was released in 1968. The movie was also released under the English title Sweden Heaven and Hell.

In 1969, Henri Salvador recorded a variation titled "Mais Non, Mais Non" ("But No, But No"), with lyrics he had written in French to Umiliani's tune.

The song became familiar to many from its renditions by the Muppets on national television. On November 30, 1969, "Mahna Mahna" was performed on the The Ed Sullivan Show by a Muppet also known as Mahna Mahna, and the Snowths. Also in 1969, "Mahna Mahna" was performed on Sesame Street by a character that was later known as Bip Bipadotta, along with two Anything Muppet girls.

"Mahna Mahna" - Jim Henson was the voice of the singing Muppet.