That's one of the most frustrating things a genealogist faces- finding an ancestor who has changed his name. I know: I had one, and it took me near 40 years and a lot of serendipty to find his name. But I did, and hopefully, so can you.
What you need to find is the ship on which he came. That is the clue for most. On it should be records of the passengers, and hopefully he will have recorded or HAD recorded his real name.
If you do not know the name of the ship, you can still search through immigration records. It might take some time, if you don't know the appoximate year he arrived.
Many people who changed their names didn't do it deliberately. They were illiterate and someone else wrote it down for them. My ancestor came from Chile and his surname was Alderete. It was recorded (in various forms) as Alterator. It was still close enough to Alderete to be recognisable as the same name once I saw it. So, if your ancestor's name was changed by someone else, you might be able to guess its true form by looking at surnames from the country he came from.
Others, for reasons of their own, changed their names themselves. Sometimes they just do small changes (a relative of ours changed his from -io to -i ending). Some are radical. A relative of my husband's took his wife's surname, because he was afraid of persecution. It was alsmost the same as his own, but a translation. That is a good place to start. A name like Hart, might be a translation of Herz, White might be Bianco and so on.
Hope this helps. If you want to, put his name up and whatever info you have on him (origin etc). I might get a better idea. Cheers.