If the order doesn't specify that she take back her maiden name, she can continue to use the married name. He can't force her not to use it, and it's up to her. Just like it was up to both of them if anyone would change their name when they married.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
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