Is it possible that US DHS denies an entry to a passport holder eligible to enter the US with ESTA if he doesn't submit his other nationality on the online format? I mean, It may depend on the context because they wouldn't probably suspect a "Mathieu" having dual french/belgian citizenship entering with a French passport and omitting to submit his own belgian citizenship in the format, but they would suspect an "Ahmed" or "Abdul" having a French citizenship and having submitted no other nationality. So in the latter case, would DHS or immigration officer enquiry further about him or simply deny him entry because of him omitting to submit his other nationality? And how can they check that he omits his other nationality other than by name?
When you apply for an ESTA (or for a visa, for that matter), you are supposed to answer all the questions honestly, and as accurately as you can.
I’m pretty sure there’s actually some text in the form that says that.
If you omit things they asked for, they may or may not catch you, but if they do, they most definitely won’t like it, and the consequences can range from a simple ESTA or visa refusal, denial of entry at the border, to an outright ban. A ban can be an explicit ban for up to 10 years, or it can be an implicit ban for life, just because they no longer trust you. I’m quite certain that in some extreme cases this can also result in fines or emprisonnent (beyond the time you will be kept in holding until they can send you back if you are denied entry).
Remember that all applications are attached to you as a person, not to any passport or citizenship you hold or may have held in the past. If you have already previously entered the US with different details, it will be trivial for them to match the two entries, at application time based on name, date and place of birth etc, or at the border when they check your fingerprints.
Attempting to lie to any immigration official is always a very, very bad idea. It will catch up with you at some point, sooner or later, and it can ruin your chances of ever entering not only the country to which you lied, but any other countries who ask if you ever were denied a visa or entry, or those who exchange data with that country. Just don’t do it.