Rebranding Question

Site URL: http://www.covenantcapture.com

I'm looking to totally tear my website up and start from scratch. I don't have subscriptions or commerce to worry about as I'm selling a service, so I'm hoping that simplifies things for my question. As part of my rebrand, I'm changing the name of my business and I'm about to purchase another domain to keep things in alignment.

Squarespace is asking if I want to add this domain to my existing site on purchase. Should I take this option, or is there a better way to handle this? For clarity sake, once the new layout is good to go, I plan on deleting the original site entirely and cancelling the plan for it's domain.