I'd probably leave the package exporting to a fixed file name and add a final File System Task (or Script Task if you prefer to write a bit of code) to do a copy/rename to your desired destination.
As far as setting the file name, I'd use a variable whose contents are defined as an expression.
Here's something to get you started:
(DT_WSTR, 50) Month(DATEADD("m",-1,getdate() ))
This currently returns the unicode string '12', which is last month as a numeric.
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