score:3
There are still a number of details missing, but you've given enough information to have a decent sense of your question. In short: do not do this.
As I understand your question, your son was previously refused entry to the United States (not deported) and now wants to visit. The ESTA form asks about previous refusals, you honestly and accurately checked yes, the ESTA was not authorized, and you now want to come up with a way to lie about it in the hope of working around this problem.
This doesn't work. Everything about US immigration law applies to him as an individual person, not simply to one of his names or passports. Here's what Customs and Border Protection has to say about this plan (emphasis addded):
If you were previously denied a visa, or previously refused entry to the United States, or previously removed from the U.S., your ESTA application will most likely be denied.
If you were allowed to board your carrier, you may be subject to additional processing upon arrival at U.S. ports of entry, and may be denied admission to the U.S. Applicants who are uncertain of whether they qualify for travel under the Visa Waiver Program (VWP) are encouraged to apply for ESTA authorization early, to allow time to apply for a visa, if needed.
Many people make the mistake of thinking that if they were denied a visa when they were a citizen of one country, then become a citizen of another country, they can travel to the U.S. under the visa waiver program using their new passport. That is wrong. The eligibility question about having been denied a visa does not ask whether or not the denial was made after you became a citizen of another country. It asks, "Have you ever been denied a visa?" - period. If you answer "No" then we determine that you have been denied a visa in the past, we consider that to be fraud, and you will be barred from entry for a number of years. It is better to admit the truth, and then apply for a visa, than go through the experience of being deported for fraud.
TL;DR: your plan amounts to fraud and could attract a lengthy ban from the United States.
Your son now needs to apply for a visa at the US Consulate serving your area. Many people who are refused ESTAs do successfully receive a US visa and are able to travel, especially if they can demonstrate strong ties that ensure they will return home. Unfortunately, it may well too late to receive one by Tuesday. It's certainly worth contacting them in the hope they can work some magic, but the process usually takes more than a couple days. I know that's not the answer you or your son want to hear, and I'm sorry for that.