If I change my name when becoming a US citizen, how does that affect my travel to my home country? At immigration, will there be any records of me at all? Or will it somehow be tied to my old name. I am escaping a bad past(political exile) and I want to start fresh with immigration there.

A name change in itself in the US does not provide any protection to escape a bad past, particularly not in a previous home country, especially if the change doesn't involve a removal of place of birth and/or no public record of becoming a citizen.

Given the increased use of technology -- including running face matching tools and other uses of databases -- escaping a bad past via a name change is increasingly failing and hasn't been a strong form of protection for many such situations for quite some years now.

Yes, you have to remember to basic general rules:

Most countries require that you enter on the passport of that country (when you are a citizen). There may be penalties for not doing so.

Secondly, the US will not provide assistance or pressure regarding a country where a dual citizen is a national.

i.e. Tunisian/American dual-national goes to Tunis and enters the country on their US passport. The Tunisian authorities notice that this person is a national and arrest them for immigration violation and subsequently find out that the person is also wanted for aiding in hiding Tunisian government funds for the ex-President's wife. Don't bother ringing the US Embassy for help.

Nothing against Tunisia, it is just that I was there last week and needed to use a country in my example.

In countries where Military service is/was mandatory, this is also a classic where a returning national thought that entering with their US passport wouldd keep them from being thrown in jail for avoiding military service and they are very surprised when they ring the US Embassy from jail and find out they are on their own.

Yes, many countries expect or require their citizens to enter the country on a passport of that country. Not all, though �.the UK and New Zealand do not, for example. The UK, for instance, merely requires that the documents presented at the time of immigration are valid for the intended purpose of the visit/stay.

All of that aside, whether another country would recognise that Bill Smith or Mary Brown is the same person as the newly re-named Bill Jones or Mary White would depend, I suppose, on their databases and how flexible they are.

Simply no substitute for talking to your immigration lawyer instead of some strangers on the internet, especially where your life or freedom may be at state. Welcome to America, and I hope you build a wonderful new life here. But build on solid ground. Discuss this carefully with your attorney.

Get advice from a lawyer specializing in such issues. However, I wonder whether it might be better and safer to avoid travel to your home country, although I understand that family emergencies might make it unavoidable. Note that some countries claim all former citizens as citizens so that you cannot revoke your (former) nationality for certain purposes, including military service.

Nobody can provide an answer without knowing which country it is. It is that country's policy that matters, not the US'.

Assuming that you...

...want/have to use your home country documents (which is apparently not your case): You may have a conflict if your home country enforces the same elements as the US, such as advanced information. For partially different names, airlines can accept multiple identities at check-in but not booking. For totally different names, you simply cannot board one round-trip itinerary at all. And if your home country prohibits dual nationality, you may need to hide your US citizenship by using two separate itineraries with a stop in a third country.

...want to hide your identity from your home country: The US passport must contain your place of birth and date of birth. (The Japanese passport, e.g. does not contain POB.) These may be too much already (if not also the technology mentioned by other posters) to get you questioned.

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.

US passports don't include long-discarded prior names used unless a passport holder requested and received an amendment/endorsement to have such, and even then it's not generally done. And generally there is no indication of name change on the passport.

I am not sure what all of the current standard is for US passports with regard to place of birth, but for a long time it was standard to refuse any request to have no place of birth listed. Some US citizens have no known birth place and some don't even have a known birthdate, but as I haven't run into a need previously to run this by counsel ever before I don't know what is done for that currently.

Political exile or identity theft? Get your story straight.
OP's earlier thread

Haiti. They just adopted dual nationality the other day.

Instead of using country of Birth, I will be using city of birth. It makes it less obvious.

Just because I speak on the first person doesn't mean the information I am seeking is mine, Just so you know.

I don't have time to lose saying "my grandmother's brother" "My father's cousin's brother in law".

I just use I for all of them. Believe what you want. If you can't help, don't bother clicking on the post, and STOP stalking people.

Well, anyway, I don't think that political exile and identity theft are completely mutually exclusive, are they?