Apple care transfer

Applecare can be transferred to another owner for a particular hardware item (e.g., selling to a new owner), or an identical item (e.g., exchange for different color).

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

Click on this link to learn how to cancel your AppleCare plan --> https://support.apple.com/HT202704

Cancel it if you do not want it, or if you are selling it the new owner may be interested in having it as part of the package and you can recoup the remaining value as well as make your used iMac more attractive in a sale.

No, AppleCare is attached to a specific piece of hardware and not it's owner. In short, it can be transfered if you sell or give away the Mac however it cannot be transferrred to another Mac.