Regional variations on nursery rhymes are quite common, I think.
For instance, where I was brought up we had:
Ding dong bell,
pussy's in the well.
Who put him in? Little Tommy Thin.
Who pulled him out? Little Tommy Stout ...etc......
(as you can see , this rhymes...)
but round here, where I now live, people say
Who put him in ? Little Johnny Green.
Who pulled him out? Little Tommy Stout...... etc
('Green' doesn't rhyme with 'in')
However, Wikipedia says 'Flynn' which does rhyme!