One form of the name 'Richman' was originally Rutzina or Ritzina, which originated in Poland. When Louis Richman's father came through Ellis Island in second decade of the 20th century, the immigration officials wrote his surname as Richman.
Another origin of the name 'Richman' (perhaps more common in the English-speaking world) comes from a corruption (or variant spelling) of the English name 'Richmond'.
This alternate spelling of 'Richmond' seems to have begun in the late 16th/early 17th century throughout England, when written records begin to appear more often. Many other variant forms (including Richmonde, Richmande, Richemond, Richeman, etc.) also appeared throughout the 'early modern' English period (basically, the 16th to 18th centuries). As spelling did not become formalized or 'fixed' until the late 18th century, any word (not just surnames) could be spelt in a myriad of fashions, perhaps most often conforming to the writer's dialectal version of its pronunciation.
In fact, as late as the mid-18th century, the surnames Richmond/Richman were still being used interchangeably, with one such document (a Cambridgeshire marriage certificate in the 1730s) enters the official name of the bridegroom as 'Richmond' (as supplied by the presiding church clerk) while the bridegroom himself signed his name uses 'Richman'. It should be noted that the English broad pronunciation of the letter 'a' mean't that the actual sound of 'Richmond' and 'Richman' would be quite similar anyways.
The birth of the surname 'Richmond/Richman' began in England with the establishment of Richmond Castle, erected shortly after the English Conquest in 1066 by Count Alan of Brittany. The medieval town which sprung up around the castle became known as Richmond. The name 'Richmond' was itself a corruption of the French name 'Richemont'
Count Alan was one of the most senior followers of William the Conqueror and he became one of the largest feudal landholders in England after the Conquest, receiving vast swathes of lands throughout England after 1066, in recognition of his military services to by King William. His primary seat was Richmond Castle but the other manorial lands he held were widely distributed throughout the rest of England, in the counties of Cambridgeshire, Dorset, Essex, Hampshire, Lincolnshire, Hertfordshire, Norfolk, Northamptonshire, Nottinghamshire and Suffolk. Together, this collection of manorial lands came to be known as 'the Honour of Richmond". Throughout the following centuries, the ownership of these lands passed back and forth between the monarch and various Engish subjects who fell into his favour.
The result of the wide manor distribution within the 'the Honour of Richmond' mean't that the word 'Richmond' began to appear in other parts of England where these manors were located. There were not only the obvious official names such as 'Richmond Manor' (as at Richmond Manor at Bassingbourn in Cambridgeshire), but also other manor-related geographic features such as 'Richmond Farm', 'Richmond Woods', 'Richmond Mill', 'Richmond Field', etc..
More importantly, beginning probably in the 13th centuries, if not earlier, the villeins or 'serfs' who belonged to the various Richmond manorial estates throughout England were starting to take the name of their manor as a way to distinguish themselves from other persons with the same given name. So John, a serf at a Richmond manor in Norfolk became known as 'John of Richmond Manor' or simply 'John of Richmond'. Finally, throughout the ensuing centuries, this would simply become 'John Richmond', even long after they lost their association with the original manor. .