Caroline's oldest son was named Cornelius Hezekiah Baker, It is possible her father was named Hezekiah or Cornelius. Cornelius is listed with Michell and Caroline in 1850 under the name Gearwar. Why he went the rest of his life as Baker, I don't know. Options include:
1. He was illegitimate, not the son of Mitchell Gearwar.
2. Feud with his dad, took his mother's maiden name.
3. Thought Gearwar unfashionable and foreign sounding, so went by Baker.
4. Grandfather had no male heirs, so Caroline's oldest son took his name in order to inherit.
In any regard, Cornelius may have been named after his grandfather, so check Cornelius or Hezekiah. Good Luck! Shelley