The current version of Zen Cart does indeed pass an identifier.
(It can't pass the order number because the order number doesn't exist yet when payment is collected. But it does the following instead ... )
Since v1.5.0 it sets the invoice number to "XX-YYYYYYY-ZZZZZZZZZZ" where XX = customer ID number in your store, YYYYYYYY is the date, and ZZZZZZZZ is your store name.
It also passes a custom field in the format of "EC-XX-YYYYYYY", where "EC-" is always present, and XX and YYYYYYY are customer number and date respectively.
Both allow for matching things up in reports etc.
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