Hi,
I'm not aware of such method to rename the purchase information, you can confirm this with your local customer service:
http://support.microsoft.com/gp/customer-service-phone-numbers/en-us
A method to tell which product key is installed on one PC, is to check the last five digits of the product key associated with the installation on that PC:
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Go to the PC that has Office 2013 installed
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Right click the Windows icon and select Command Prompt.
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Enter the appropriate command:
For 32 bit Windows:
cscript C:\Program Files\Microsoft Office\Office15\OSPP.VBS /dstatus
For 64 bit Windows:
cscript C:\Program Files (x86)\Microsoft Office\Office15\OSPP.VBS /dstatus
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The command prompt box will show you the last five digits of the product key associated with the installation on that PC.
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Make a note of the PC the Office 2013 product is installed on, and five digit number. You will need this for reference.
More information about How to find your Office 2013 product key after installation:
https://support.office.microsoft.com/en-us/article/How-to-find-your-Office-2013-product-key-after-installation-026bc81b-6b2f-4052-b433-f41e6cc31c5a?CorrelationId=c0522590-aa70-46f3-9fba-9c91bf2d4ea2&ui=en-US&rs=en-US&ad=US
Actually for multiple users, I recommend Volume Licensing to activate Office, which is much easier to manage:
http://www.microsoft.com/licensing/about-licensing/office.aspx
Regards,
Melon Chen
TechNet Community Support