i suppose it depends on the details, but if you're asked for state-issued identification when processing a return, and you present a falsified document that purports to be state-issued, that's a almost certainly a crime. (even the creation of such a falsified document is likely a crime.)
I presume that the parent post refers not to forged documents but to obtaining legitimate identification under a different name/alias - which is generally allowed in common law countries, where you can choose and use any name you wish, as long as you are not trying to defraud someone (e.g. here's a case example from Massachusets http://masscases.com/cases/sjc/320/320mass448.html "If acting for an honest purpose, one may lawfully use a name other than his legal name without procuring a change of name").
The question there is whether avoiding a ban on returns would count as a honest purpose; arguably it would not. A standard example for inappropriate name change is changing the name to avoid seekers of debt repayment using the previous name, this seems similar in intent.
avoiding a ban on returns should certainly be considered fraudulant - you're banned by the store's policy, which you would have agreed to when purchasing.
