Do you have any authority for your notion that a corporation's holding premises open to the public under an assumed name, and offering tenants the opportunity to rent units within the mall operating under that assumed name, does not constitute transacting business under that name? Please post it when you find it.

The issue of non-registration relates to his original mistake in identifying the defendant. He has corrected the issue and, if necessary, he can point out the failure to register to the court in response to the defendant's argument that the lawsuit should be time-barred.