There are so many variables that without knowing specifics, it's impossible to give an opinion.
Does your home country have a single citizenship, meaning that you autoatically cease to be a citizen of that country when you are naturalised in the U.S?
Or does your home country continue to claim you as a citizen?
Will you need a visa to visit your home country?
If you need a visa, your home country may require you to give all names used and, of course the place of birth.
It also may require you to furnish details of your former citizenship, or proof of abandoning your former citizenship.
Are you subject to mandatory military service in that country?
Some countries require your father's name.
Your U.S. passport will have place of birth on it. You will also be required to furnish all names used when applying for a U.S. passport. I don't know if your former name(s) appear on the passport, or whether the passport will give anyy indication that you had other names.
If they are actively looking for you, it will be difficult for you to slip in an out. On the other hand, if you were not a big fish, you could probably slip in and out without being caught.