While we could think in strictly military terms about the pros and cons of anonymity vs public knowledge, I do think it is largely irrelevant to your question.
I don't see why the public, much less the rest of the world (with the exception of the friendly forces we are working with), needs to know that information unless it's somehow relevant.
Why would the public would need to know about such things? And because you're asking that of the United States, I offer you this simple answer: because democracy.
I believe accountability is a requirement for a healthy democracy, and identification is a requirement of accountability. Would you be comfortable with a faceless, anonymous government? I wouldn't. How would you know if Minister of Agriculture has conflict-of-interest ties with agrobusiness? How would you know if Secretary of Defence is a vocal neonazi, or Secretary of Justice a rapist? That members of government are identifiable is a form of checks and balances.
The same extends to people empowered by the government to act in its name. Police officers and members of the military wear uniforms where they are (usually) identifiable. And it's also true of civil servants, which are usually required to identify themselves.
Without the ability to identify someone, the best you can do is lodge a vague complaint and hope the government will figure it.
Of course, this does not mean we should publish the full list of military personnel openly. That would probably be a bad idea, for reasons of privacy and operational security.
Accountability doesn't require that every person be identified all of the time, only that they can be identifiable when relevant. I think military commander being public figures satisfies that. You know who is ultimately responsible for the actions of the troops (not that the troops aren't also responsible of their own actions), so you have a way to check and balance their actions done in the name of your country or, in a perfectly functioning democracy, in your name.