Origin and Spelling of the Name
Most of the Crissman/Chrisman/Crisman/Cressman family trees in the U.S. came from the town of Pfungstadt, Germany [http://en.wikipedia.org/wiki/Pfungstadt]. The Cressman family association maintains that the most faithful german spelling of the name is "Crößsmann", still used by many of the residents of Pfungstadt today.
In writing the German, it is common to write "ö" as "oe", dropping the umlaut. Also, the "ß" serves as an "s", and was thus written as "Croefsman" in colonial English script, or "Croessmann" in the modern style. The attempt to translate the German to English when these immigrants reached America quickly produced a wide variety of mutations, including Crissman, Chrisman, Crisman, Cressman, Croesman, and Christman. Also, the letters "C", "K", "G", and "Ch" are often interchanged when the German is translated.
As one typical example of the variations in spelling, consider this case. An immigrant ancestor's name is seen spelled in records in the U.S. as "Crössmann", "Greesman", "Creesman", "Crossman", "Croesman", "Krössman", "Crösman", "Gryzeman", "Grossman", and "Croesmann". He had three sons. Descendants of the eldest son predominately use the spellings Crisman and Crissman. Desendants of the second son use Cressman. And descendants of the third son today use the spellings Chrisman and Chriesman. Despite these many spellings, these are all from the same line, from the same immigrant ancestor.