So I went through every version on this thread. Now, I grew up with the "Flat Rock Ballads" recording by Carl Sandburg, in which he punctuates the repeated verse (always the same verse, nothing cumulative or changing) with every kind of laughter there is: belly laughs, chuckles, guffaws, humming laughter with closed lips, giggles, catty purring growls....this is all absolutely FASCINATING to a very small child. We kids ended up giggling right along with Sandburg.

Many of the versions on this thread differ from Sandburg's singing.
This is what I remember:

My name is Yon Yonson
I come from Visconsin
I work in da lumber-mill dere (insert laughter)
Ven I go up da street
Da people I meet dey say:

"Vat's your name?"
an' I say.....