Dual Citizen - ESTA - Travel with stops in USA - Visited Iran

There is a simple rule (which we always advise you should follow):
Never lie to border officials.
And that include automated systems.

If they catch you on not disclosing you have been in Iran (and you did already mention it yourself when you first applied for your ESTA) you can be banned for a long time, not just in the USA but also in countries that work together with them like Australia and the UK.

Better find a flight not including a stop in the USA or apply for a visa. As you have been in Iran a few years ago, you might get a visa without problems. But once you have been caught on a lie you will never be trusted anymore. After a ban you may still have trouble getting visa.

Using a different passport may be enough to fool them but that is not a given, it may well be that they combine your name, date of birth, place of birth and other details. And even if there are differences in the details, there might be enough for them to combine the information and work out you are the same person with a different passport.

Your problem is not that they might link your Italian passport to your Brazilian one and might somehow know that you used the Brazilian passport to travel to Iran; the problem is that they will link your first ESTA application to your second one, because you are using the same passport for both applications, and they will see the change in your answer.

I would not be at all surprised if your second application is denied solely because of your answer on the first application. However, even if your second application is not denied, you run a significant risk of being asked by the immigration officer at the US border to explain why you submitted two applications with different answers. If it comes out that you have in fact been to Iran, you will be found inadmissible to the US and sent back to Brazil with a lifetime ban for misrepresentation.

US immigration officers have much more experience conducting interrogations than you likely do being interrogated, so the likelihood of your being able to keep this fact concealed if they decide to interrogate you is very small indeed.

By contrast, if your second application is denied, you're still in a very bad spot. What would you do in this case -- apply for a visa? If you do, the visa officer is likely to ask about your differing ESTA answers, and that is likely to lead to lifetime inadmissibility for misrepresentation.

A much better plan is to apply for a visa now, without making any misrepresentations, so there will be no reason to refuse the visa.

Don't lie on immigration applications. Many people have successfully obtained long term U.S. visas after visiting countries that make them ineligible under VWP.

Will I have a problem if I apply the ESTA again answering that I haven't been in Iran?

A willful misrepresentation will result in a permanent bar to the United States. There is no time limit; a permanent bar can be applied even if discovered after 20 years. It is trivial to connect two documents with the same or similar names and dates of birth.