Does the US government know if I have another passport?

The U.S. government does not in general know whether you have another passport, nor does the U.S. government care that you have another passport.

Occasionally they could know, for example, if Customs searches your bags during entry and finds the other passports. But that is a rare case.

It depends in part on your place of birth. If you were born outside the USA, then your parents would have filed a registration of foreign birth, so the USA would then know you could have dual citizenship. You also have to supply proof of citizenship, along with your parents birth countries when you applied for your US passport. So the government could know you might have a 2nd passport and/or dual citizenship.

Would they care? For the most part no, unless your birth country warrants watching or if your family name warranted watching.

Massive amounts of data are mined by governments all over the world. But most just sits in databases only to be pulled up when enough values match an issue at hand.

Is there a reason you are concerned about the 2nd passport being revealed?

A lot would depend on whether the countries share data, whether you actually use both passports, and how you use them.

By now, governments have noticed that one person can have alternative names, so merely matching on name, qualified by date and place of birth, is not good enough. There is a general and increasing trend to depend on biometrics, typically some combination of fingerprints and photographs that allow analysis of the structure of the person's face.

For example, if you enter the US on a non-US passport, DHS collects fingerprints and a photo, with a few exceptions such as diplomats and children.

Yes, they will find out. And in addition, you cannot have a security clearance and passports from different countries, this violates ITAR which are laws which make it illegal to speak about the USA to other countries (and vice versa) regarding sensitive or classified information. So if you're looking to get a security clearance, do not have more than one passport, that makes you a citizen of more than one country which in itself is not illegal in most cases, if we have an agreement with that country, but it does make it impossible to gain a security clearance.