Changing name of domain for child/parent

Hi all,

I have a parent domain called company.local and a child domain called europe.company.local

The company name is changing and so we have to rename our parent and child domains, eg: newcompany.local and europe.newcompany.local

This is a change I have never had experience in, and I'm not even sure where to start Googling. Does anyone have any links I could read as a place to start, or even just terms that I should be Googling. I guess I will also need to think about DNS and our Certificate server too.

I am presuming I can't just go into my domain controller and rename it, so any tips about how to proceed will be gratefully received!