I've been reading about this, and although similar questions have been asked, I got mixed signals, and often concerning situations slightly different to mine.
Essentially, if I will travel to the US and want to obtain a Visa or an ESTA, I am asked whether "I have ever been issued a passport by another country" and where.
In my case, I am applying as a citizen of country A, but I also hold a citizenship to country B. If put a no in that field, is it possible that the US could find out I actually have passport B through some online database or information-sharing scheme, and if so, could that lead to trouble?
I may prefer not to specify the second passport for various reasons, including that I don't have the passport on hand, or that I may want to keep the passports separate for situations like travelling to certain countries. For example, I heard there's a bit of trouble if you want to travel to both Iran and Israel in one lifetime, and to avoid that one could use different passports when travelling to each. This clearly wouldn't work if everyone knows you have two passports and can ask for the other one as well. Also, I haven't yet traveled to any of those places, this is more of a just in case consideration.
Also, what if countries A and B are for example in NATO/EU and have treaties and friendly relations with the US; does that increase the chance that the information has been shared?