Open your account and disable the old subscription for the old PC name.
Choose download and install it on your new PC BUT do not have both PCs the same name that will be a mess.
That should work
Please follow the below instructions for deactivating the subscription on one PC and to reactivate on another ;
To deactivate a license from your current McAfee subscription and release the license for use with a different computer, use the steps below:
1.Go to http://www.mcafee.com.
2.Click Home and Home Office.
3.Log in using the email address and password you used to purchase your McAfee software.
4.Under the My Protection Products section, select the subscription from which you would like a license released
This will take you to the list of machines currently being protected by McAfee.
5.Find the computer you want to deactivate and click the Deactivate button to the right
You will receive a warning asking if you are sure you wish to continue with the deactivation of the selected machine.
6.If you selected this machine in error, click Cancel. Otherwise click Deactivate to proceed.
After you have successfully deactivated the license, you will be returned to the same screen but the button will now say Reactivate
7. Post this on the new PC reinstall the same suite and once its installed everything should be set right .