If your computer is UEFI Bios (most name brand computers from the last few years are), the Windows License is Embedded in the Bios.
If you have a Windows 10 Pro license, you can go to S*ettings/Update & Security/Activation* and type in your Pro License to convert your Home version to Pro. If you signed in with a Microsoft Account, Microsoft has your Windows Home License in it's Database. If you type in a Pro license, it will convert your Windows license in the database for your Microsoft Account.
If you want to view your Home license and write it down, you can use Belarc Advisor.
Cloning produces an exact copy. If losing keys, or licenses is a concern, install Belarc Advisor on the drive to be copied first. https://www.belarc.com/AdvisorDownload .doing so will insure access to that information.
Am not sure I understand the question exactly, so here's my best shot. If you are referencing the drive in the old computer, no need to remove the OS, if you simply want to erase the data so it can be reused by someone else just reset the computer.
If on the other hand you are concerned about the existing OS on the drive in the destination computer, yes you may remove the OS from it as it will no longer be your boot drive.
In hopes this information helps.
Download Belarc Advisor, run it, report back the motherboard board model.
If he self built it, Belarc should identify the model