You seem to be a little inconsistent with your variable names between the two code examples, $todayDate in one and $today_date in the other, so you may have a typo in your script. I don't know how you initialise your $todayDate variable. If you generate it programmatically in your code rather than reading it from a file you may find the strftime() function of the POSIX module along with localtime and time useful.

$ perl -MPOSIX=strftime -E '
> $file_dir = q{/var/log};
> say strftime qq{$file_dir/filename1.log.%F}, localtime( time() );'
/var/log/filename1.log.2012-08-08
$
[download]

I hope this is helpful.