The disclosure is not made for the average person, first of all. It's made for the office. Only the portions that have to be disclosed and put on the public record will be put on the public record.
Obviously, if you have a numbered company that also operates under a name, it would be appropriate to disclose both. If you don't do that.... As I mentioned before, each person appointed gets a counsellor to advise them. The counsellor will certainly ask you, “You own 3509 Limited. Does this company operate under a trade name or not?” Therefore, it would be disclosed.