Childrens Book: character's name is "Give me the Ax"

I'm trying to remember the title of a children's book or book collection that had a character named "Give me the ax". It's a story about these kids that are born and the parents decide to wait and let them name themselves. So as time goes on one chooses the name, "Give me the axe." The sibling has an equally odd self given name. The children's names help seal the parent's fate. I remember reading this about the same time I read about Paul Bunyan. I'm in my mid 40's and would have read this book when I was 8 - 10 years old.

This is a story called "How they broke away to go to Rootabaga Country" by Carl Sandburg. I have it in a collection called The Junior Classics - its in Volume 2 Stories of Wonder and Magic.

>2 Darth-Heather: Dang, well identified! Story available to read online here:

https://americanliterature.com/author/carl-sandburg/short-story/how-they-broke-a...

Google tells me this story first appeared as part of Rootabaga Stories (1922). A sequel also published: Rootabaga Pigeons (1923). All of the stories seem to be set in same absurd world, with reoccurring characters.

There are some differences to the OP description though:

Gimme the Ax lived in a house where everything is the same as it always was. (...)

So he decided to let his children name themselves.

“The first words they speak as soon as they learn to make words shall be their names,” he said. “They shall name themselves.”

When the first boy came to the house of Gimme the Ax, he was named Please Gimme. When the first girl came she was named Ax Me No Questions.

And my skimmed-read didn't spot anything about the siblings' names sealing their parent(s)' fate. Unless that happened in one of the other stories?