Normally, I would say that it is impossible to end up having Windows 10 Home installed when using the Windows 10 Pro installation media, but I may have an explanation to what has happened.
First, make sure you have indeed used the Windows 10 Pro installation media. If you are not completely sure, you can run the Windows 10 media creation tool and select to create the ISO file for Windows 10 Pro, which you can then burn onto a blank DVD. Use that DVD to re-install Windows 10.
In case you still end up having Windows 10 Home installed, just leave it as it is for about 2-3 days. During that period, your Windows 10 computer will periodically contact the activation server to verify the activation. It is possible that it will automatically convert to Windows 10 Pro without you doing anything special.
I am suggesting you that because similar issue appeared for many people who decided to upgrade to Windows 10 right after it became available. After the upgrade, their copy did not automatically activate. However, after about 2-3 days, the activation was successful.
When asked Microsoft why that happened, their response was that the activation servers were overloaded and could not process every activation request right away. I know it has been several months now since Windows 10 came out and the activation servers could not be overloaded all the time, but that is my explanation to this problem as I don't see any other.
If your copy of Windows 10 doesn't convert to the Pro edition after 3 days, you can contact the Microsoft support again. I do not have a direct contact for a supervisor, but that might not be needed. You can explain the issue to a general Microsoft representative who answers your call. Just make sure to tell them the order ID of your Windows 10 upgrade purchase. If that is not enough, you can ask them where to send a proof or purchase. When sent, such information should be forwarded to a supervisor for inspection. When they confirm you indeed purchased a Windows 10 Pro upgrade, I believe they will correct the issue on the activation server so that your digital entitlement could be properly recognized, or they will send you a Windows 10 Pro product key to manually convert the Windows 10 Home installation to Pro.
You can call the Microsoft Store department directly on this number:
Dial 3 to connect with a representative.
Let me know how that went.