Apple cloud computing recognizes device even if replaced

I had my latest version of Apple phone replaced because I am under the impression that the echo issue is a factory defect. When I updated my data from my stored data on Apple’s cloud computed, the system is assuming that what I am doing is storing another set of data from another phone, hence, I no longer have additional space for my cloud computing for other data.
Can you please tell me how to remove these data so that I can allocate space for my new phone without removing any information?
I maintained the phone name, I called the Apple customer service and they said that this is happening because the cloud computing has identified me based on the serial number, but my question was never answered. Please guide me through the process. Thank you.
