Can you buy a brand new MacBook Pro for someone else?

Yes, whoever sets it up with their Apple ID is de facto the owner. However, if you also buy AppleCare then you may wish to formally transfer the ownership to the actual owner, although it doesn't matter too much because the AppleCare is linked to the machine, not a person. It just means they will receive the communications about it from Apple instead of you.

Click on this link to read how to 'Transfer your AppleCare plan' --> https://support.apple.com/HT202712

One slight consideration is a remote situation where if that person need to take the device to Apple to undo a Firmware lock. In that case Apple will want to see they are the true owner which is a receipt in the name of the person taking the device to Apple. Either that, or a legally documented trail of ownership. Basically that that person isn't a thief trying to bluster Apple into unlocking a security feature. In the case of a deceased owner this is done with a court issued document. Anyway, the lielihood is remote but is once case where it really helps for that person to have their name on the receipt instead of having to figure out what Apple will need to prove they are the owner. This is more common with mobile devices that has an activation lock set on them.