In England the name, Crosman, can be found with the spelling Crossman, Crosseman, Crosman, Croseman, Croixman, Croisman, Croxman, Corceman, Crossman, Crossemen, Crosmen, Crossmann, Crosmann, Crouceman, Croiceman, Croseman, and these changes in spelling frequently occurred between father and son. There is a record of a father and eight sons, and in the graveyard where they are buried, all nine have different spellings. Many reasons existed for these variations, but mainly it was because church officials and scribes spelt the name the best they could as the individuals themselves could not write.
In the United States those with this surname typically spell it with one or two 'S's. Does the spelling have any significance? If you use two 's's do you come from one line while those with only one come from another?
That doesn't appear to be the case. The early Connecticut Crosmans were illiterate. They could not write their names. The early vital records of Lyme, New London, Connecticut describe the mark of John and Elizabeth Crosman. Yes, one 's'. This spelling was created by the clerk who recorded the names. Their son, Thomas, spelt it with one 's' in his application for a Revolutionary War pension. Thomas' sons spelt it both ways. The one that spelt it with one 's' had sons who spelt it both ways. This also appears to be the case with the Massachusetts Crosmans although many more of them may spell it with one 's'.
Your name could be Crossman or Crosman and still be directly related to a 'Crosman' with another spelling.
Why did one 's' Crosmans decide to use the two 's' spelling? I can only speculate. I'm a one 's' Crosman and I've spent my entire life trying to get people, the government and employers to spell it correctly. Perhaps those that changed found it easier to use two 'S's instead of one. Or, perhaps some school teacher convinced them that 'Cross' was spelled with 2 and therefore their surname should be also.