Domain Name Change - Same Server

Quick question, most of the searches I found are slightly different than what I'm looking to do, at least I think.

Sytist 3.7.2 installation, need to change the domain name ONLY (and DNS records). Currently a live site, will be using the WHM/cPanel 'modify an account' option. Sytist is run out of the /public-html/ directory. Basically keeping the old install alive for 6 months or so for customers to see/purchase older event images.

So...3.7.2 install is h-p.com. Changing it to h-p2.com. Same IP address, etc. Does my Sytist admin login auto get recognized as h-p2.com/sy-admin/ (or what I set it to)? Any other mods needed from that Sytist setup?

New install, 4.6.0 Sytist, will become h-p.com, different hosting company, install ~98% ready for DNS records change.

Thanks for the help!

You just need to change the domain name in the URLs you are using. Nothing else to do. When you use the new domain in the admin, the URLs automatically use the new domain.