There are a few ways to do this. I don't have all the details but here are a few ideas:

The most simple way would be to create a second company in Odoo and work in a multi company environment. You can activate this in General Settings. Users would have to switch between companies to get the correct report. Make sure that the old data is related to the old company and the new data to the new one. The standard variable for this is company_id.

In QWeb Reports there is a parameter called attachment_use which saves the document after it is generated so that future "Print" requests will use the original version instead of generating a new one.  After setting this to True you could write a script to generate every document of the Old company, and after that you could change the company's name in Odoo. I think this could bring some problems in the future in case you need to modify something old.

Another solution would be to apply some logic in the template that creates the report header. There is already some logic inside it, and it is usually imported by other reports. Look for the external_layout View that your company is using (Settings/Technical/Views). You could probably apply som "if data is old" condition to select the company.