Renaming a file via a batch file

I run a system that creates a log file after the nightly back ups run. I want to use a batch file in DOS that runs via an AT job. I want the batch to move the log file (which I know how to do), and I need to rename the file as well. If possible, I want it named whatever the current date is. Is there some way to do this, or is there a way to create a list for the file to pick from, I.e. an “if/then” kinda thing?