Renewing certificate

What happens when certificate is being renewed? Specially with the files that have to exist on domains to prove the ownership (those files with GUID-like name and key inside)? Do they change (need new files with new names and keys) or are those original (when first certificate request) enough?

I’m thinking about a bit more complex scenario. I have both Windows (IIS) and Ubuntu (nginx, apache) servers and a bloody single IP (thanks to the ISP). So I need a common entry point to handle both OS. I don’t think client will be able to handle this scenario, but that’s fine.
So I am thinking about solving it by myself. I’d automate creation of those files if necessary (if they need to be recreated on each renewal, that is). Otherwise it isn’t that important.