I see that on page 312, you use methods with under scores. For example, change_price_to. On page 317 you use UpperCamelCase.

Do you think any special style helps domain design easy? It may look like a stupid question, but think about how this can help new developers or large teams?

In my opinion it's mostly it's based on team and language conventions. When I write scala I use lowerCamelCase. In .NET I use UpperCamelCase and in python I use snake_case to follow community conventions and language style guides.

Mostly in the book we followed the .NET convention of UpperCamelCase, but as you point out we used snake_case in a few places because it does make expressing certain phrases easier to read.

It can make your codebase too inconsistent when you mix different types of casing so it's best to use one or the other consistently in my opinion. But if you think there is a big benefit to using a differing casing in certain places, it's worth considering.