iCloud account

As per this article Set up your MacBook Pro - Apple Support

• Sign in with your Apple ID: Your Apple ID consists of an email address and a password. It’s the account you use for everything you do with Apple—including using the App Store, Apple TV app, Apple Book Store, iCloud, Messages, and more. Sign in with the same Apple ID to use any Apple service, on any device—whether it’s your computer, iOS device, iPadOS device, or Apple Watch. It’s best to have your own Apple ID and not share it. If you don’t already have an Apple ID, you can create one during setup (it’s free). See Apple Account on Mac.

You can have a different Apple ID and password on a new Mac ( create a web mail address using some mail services like gmail or any ) and sign in Sign in with your Apple ID - Apple Support with the new Apple ID and its password with different account credentials How to create a new Apple ID - Apple Support

To your second part of the question -

I asked the above question and realized that my iPhone is also on the cloud. So it would make more sense if I keep the first iCloud account on my new computer so it is synced with my phone .

the iPhone is synced to old Mac having same Apple ID and password on the same network .

You have to change apple id in iPhone ( have to set new Apple ID and password used in new Mac ) so that it syncs ) .

See the articles sign out Apple ID from iPhone Sign out of iCloud on your iPhone, iPad, iPod touch, Apple TV, or Mac - Apple Support

And sign in with new Apple ID and password of your Mac Sign in with your Apple ID - Apple Support

On my old computer I have a couple of apps that can't be updated to go on my new computer - you have to use migration assistant Transfer your data to your new MacBook Pro - Apple Support

Transfer your information to Mac from another computer or device - Apple Support