If your ancestor changed his name in the United States before 1900, chances are it was unofficial and done "without paperwork." Proof of the name change may be indicated on a deed or in an estate settlement where the individual is referenced by a former and the current name.
In some situations there may be no direct document linking the two individuals. Some name changes were done in a court of record, but many were not.
My children's ancestor was born William Frame in Chicago in 1888. For reasons that are currently unknown, he took the name William Apgar by the time he married. There's a chance he was adopted, but even if he was in that era the adoption likely would not have left any records either.