The spelling of my mother's surname changed after she was born, as did that of her first name. The new spelling was standardized, one might say, when my grandfather was naturalized in the 1930s and is used to this day.
My father and his brothers changed their last name without going through the courts in the 1940s. Because Dad did not report the change to Social Security, he had to get an affidavit from someone who knew him with both names before he could draw on his Social Security retirement, a minor issue. But his new name was used in all his US Army documents dating back to 1941.
There is no requirement to have a name "legally" changed as long as it is not used to defraud.