Marsh is of English origin and means "from the marsh". It was originally used as a surname for someone who lived near a marsh, but has since evolved into a given name.
"Marsh appears to have been a popular name for newborns throughout much of the 20th century, with peaks in popularity around the 1950s and again in the late 1960s to early 1970s. However, it seems to have fallen out of favor by the late 1980s, with fewer than five births recorded each year since then, until a slight resurgence in recent years."