As always, it is not that literal in actual etymology. Christmann is the most cases derived from the given name Christian, shortened to Christ and than suffixed with "mann"—thus a man belonging to the household of Chris, maybe a descendant. The name has a striking geographic concentration in southwestern Germany (Pfalz and Rheinhessen regions of Rhineland-Palatinate). Chrismann is an attested variant of Christmann, it probably lost its last n on American soil.
See:
Dräger, Kathrin, Christmann, in: Digitales Familiennamenwörterbuch Deutschlands,
URL: <
http://www.namenforschung.net/id/name/1042/1 >