There was not a Mighty Man whose named started with the letter C, but there was a town called Carmel and Carmel has significance to the story of David.
A man named Nabal of Carmel was "surly and mean in his dealings." He had a wife, Abigail, who was "intelligent and beautiful." Nabal's men and David's men exchanged words, which quickly escalated to drawing swords and spears, and it took the calmness of Abigail to prevent bloodshed.
When it all shook out, Nabal died after Abigail told him all she'd done to make peace with Nabal's enemies, and Abigail then became David's wife.
That Carmel produced a Mighty Man named Hezro. We don't know anything else about Hezro, a Carmelite, except that he was counted among the Thirty. Perhaps Hezro had had surly and mean dealings with Nabal and it was easy for him to cross over to David's team? Who knows, but isn't it a juicy story?
You can read more about David and Nabal and Abigail in 1 Samuel 25.
C is for Carmel and Hezro, the Carmelite.