This silly but catchy song was written by American singer Shirley Ellis with Lincoln Chase. (It can’t have been hard to write as there are only a couple of notes in it.) It was released in late 1964 and went to No 3 in the US. I am not sure if it was released in Britain but if it was it did nothing. I think it must have been released here because I still get the annoying words on the brain occasionally.
If you are interested, Wikipedia explains how the game works.
Using the name Katie as an example, the song follows this pattern:
Katie, Katie, bo-batie,
Fee fi mo-matie
A verse can be created for any name with stress on the first syllable, with X as the name and Y as the name without the first consonant sound (if it begins with a consonant), as follows:
(X), (X), bo-b (Y)
Bonana-fanna fo-f (Y)
Fee fi mo-m (Y)
And if the name starts with a b, f, or m, that sound simply is not repeated. For example: Billy becomes “Billy Billy bo-illy“; Fred becomes “bonana fanna fo-red“; Marsha becomes “fee fi mo-arsha“.
The song gives no indication of what to do with names where the stress falls on a syllable after the first, like Renee, Maria, or Lebron.