How would you write 2 middle names?

Hi everyone, I need some advice. My son is going to be my last baby and I want to name him after my 3 grandfathers who have passed but meant the world to me. I am set on using the name so please don’t bother telling me you don’t like it or to change it. My question is if you have 2 middle names do you hyphenate or not? Doesn’t hyphenating make it easier or harder on legal documents?

The name would be written

Newton George Louis Lastname

Or

Newton George-Louis Lastname

What will be easier for legal documents? Hyphenate or no?