This originates from a comic song “Little Bingo” performed in London in c.1780, which started:

The farmer’s dog leapt o’er the stile
His name it was little Bingo

 In the 19^th century it was still being sung by adults with an accompanying dance. By this time, the song had been taken up by children as a singing game, and the dog’s name sometimes appeared as Stingo or Pingo. The singing game is rare now but it is still remembered as a nursery rhyme.

 Notes by Gwilym Davies 6 May 2015