I normally rename the test logs to include e.g. a version number for the application tested like this example: Basic API test - 06-09-2016 - 5.3.01.02 Basic API test - 07-09-2016 - 5.3.03....
Take a look here:
https://support.smartbear.com/testcomplete/docs/testing-with/log/working-with/exporting/about.html
The sections on Exporting Results From Tests and Exporting Results From the Command Line have examples that rename the log file.