The Mouchemore name had sources in Great Britain in the late 18th Century.

Many English surnames originated in the first written records kept in the villages and parishes throughout Britain. These early records were often kept poorly by scribes and record-keepers.
As many illiterate workers were recorded by their occupations, names like Baker, Hunter and Smith (blacksmith) were common. When the word "son" was also added to many surnames, names like Peterson, Harrison and Jefferson were created.
In the Dartmoor and South Hams region of the Devon district in south west Britain, early scribes routinely added the word "more" to common names like Michael and Mitchel, to describe their children, and the words "much more" to describe even more children.
In this way, names like Michaelmore, Mitchelmore, Muchmore and Mouchemore, along with many variations in spelling on the theme M*CH*MORE, were created.
The name Mouchemore first appears in the parish ledgers and baptismal records, around the early 1820s in the Dartmoor and South Hams region of Devon in Britain.
Sources
Picknowls How do you spell M*CH*MORE?
Picknowls M*CH*MORE one name study
Picknowls 14 Descendants of Peter Mouchemore