You can use Agent Tokens in your log name.

Using Tokens in Job Steps- SQL Server 2008 R2

Change the log name to something like this:

X:\...path to log files...\filename_$(ESCAPE_NONE(STRTDT))_$(ESCAPE_NONE(STRTTM)).log

And you'll get a file name like this on each run:

filename_20130305_231247.log