My ancestors always Spelled it Cother. It is the Census takers and other people who spelled it wrong. On Deed indexes in Richmond County NC it was spelled Coulter, Cothier, Cotter, Cather, Cotner to name a few.
It remains so today. My Daughter was Texas State Champion in the 100 yard dash and secon in the nation in the 220. Every Track meet they would announce the name wrong. Sometimes as Cocker others I cam totaly recall. Finally she would approach the announcer and tell him how to pronounce it. Telling them she WAS going to win so learn it. She held 16 record in south TX and else where, recieved 26 scholarship offers.The offers would come in the Mail. You guessed it Spelled wrong. By the way she was a a sophomore in HS and they were shocked . She developed Scolosis and had her Back operted on which ruined her running Career. She still attended Stephen F Austin and they went to Nationals. she dropped out in ther second year with the Pain.She had two 11 inch rods in her Back. She is well known in Track circles in TX. She is still ask to speak to HS on Determination. They still announce the name wrong unless she tells them how. She now has them use her Married name Horn. She is 42 and still in demand.All this means nothing . Just to show how names can be misselled and pronounced. I NEVER take a name as they rihgt spelling and try all ways I can conceive to look. My Cockburn ancestors are spelled Cogburn/Coggburn/Cock/Coburn and other ways.