How do the files look when you first download them? Hazel can't use dates if it doesn't have access to them. If you download a statement a month late, what information is there in the file for Hazel to glean to know that the statement was actually for a previous month?
For the case where you download the statements in the same month (i.e. the date added/modified/created corresponds roughly with the statement date), you can set up a rename pattern like:
(domain) (date created)(extension)
The (domain) attribute matches the domain you downloaded it from. This usually matches the name of the institution/bank. You can click on it and see extra options to strip off the www and .com from it. The nice thing about doing it this way is that it works if you have multiple banks you download from (like I do).
As for the date, click on it to edit its format. There, you can make it 2009-01 or whatever. Unfortunately, as I noted above, you can't do any math there so you have to find a real date associated with the file that matches with "the month before".