Might that be a business model for an enterprising Secretary of State? They carefully verify your real ID, the fake ID's trivially tie back to that if the cops ask (not so useful for committing crimes), there are upcharges for multiple fake ID's, or tweaked ages / weights / photos. More upcharges for "vanity" names...
"Really, your honor, it's hardly different from an author getting a DBA or LLC for his pen name."
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I'm aware of the culture war battles around ID cards for illegal, trans, etc. people. A reasonable, business-like SoS - trying to boost revenue while protecting people from data breaches and other such hazards - would stay far away from those minefields.
Also, it'd only be a DBA/LLC depth of "identity". Those do not give you a citizenship, nor clean police record, nor new gender, nor legal adult status, nor marriage, nor SSN/EIN, nor voting rights, nor ...