Thank you for following up with me. The legal situation is that if a person fails to give accurate information on any element of an immigration document that allows you entrance to the US, the permission to remain in the US will be revoked and that person is subject to deportation proceedings.
On top of a person being deported on a finding that he provided misleading information to USCIS that permission will receive a bar ( temporary or permanent) from reapplying for any kind of US visa in the future.
Hence, I cannot say if a name used for minimal purposes will come to light of USCIS and susbsequently to Immigration and Customs Enforcement, but it should be determined that false information was provided, you would be involuntarily deported and future US visa applications was subsequently jeopardised.
For these reasons, it would be in your interests to disclose both names.
Remember this is a statement of the law, with no form of action being encouraged by me as no attorney-client relationship can form as a result of using this third party provider.
PLEASE REMEMBER TO RATE MY RESPONSE 3 STARS TO 5 STARS BEFORE EXITING
If something remains unclear please follow up with me on your question.
Best of luck
Bill attorney at law