Good question. I am also puzzling over why these Twitchells switched to Mitchell.
My mother is a Mitchell, and a descendant of Moses Twitchell. She hardly believes her ancestors were Twitchells. But if I say so, she says, it must be right, since I am the one doing the research.
Moses - Moses5 Twitchell, b. 15 NOV 1758, Westboro, Worcester, MA, son of Moses4 and Mary Sheffield Foster. Married Dorcas Dolley. Their son William6 is also one of the name switches but skipped from your list.
William6 - born between 1789 and 1792, New Portland, Somersetl, ME, married Betsey Eaton Everett.
Eliza - Eliza7 Twitchell, b. 1812, dau of William & Betsey, married in 1834 Richard Hutchins
Lydia - Lydia7 Twitchell, b. 1815, dau. of Wm. & Betsey, m. 1838 John Whittier.
Clarisa - Clarissa7 Twitchell, b. 1813, dau of William & Betsey, m. 1839 Alvin Hayden
Cynthia - Cynthia7 Twitchell, b. 1817, dau of Wm. & Betsey, m. 1838 Ward Hutchins.
Rachel- Rachel7 Twitchell, b. 1819, dau. of Wm. & Betsey, m. Benj. Churchill.
James - James7 Twitchell, b. 1823, son of Wm. & Betsey, m. Rebecca bef. 1855.
John E - John7 Everett Twitchell, b. 1825, son of Wm. & Betsey, m. Abigail bef. 1852.
Betsey - Betsey Eaton Everett, b. 1793, dau. of Josiah and Rebekah Farrington, m. Wm. Twitchell 19 DEC 1811.
Dorcas - Dorcas is either Dorcas Dolley or Mrs. Dorcas Dolley. I am not certain. The records say Mrs. My opinion is that she was not a widow, and that her maiden name is Dolley (possibly from D'Oyley). She was born about 1760, dau. of John Dolley and Sarah Goddard. Would appreciate help with Dorcas. She married Moses Twitchell in 1781, Gray, Cumberland, Maine.
Mark - Marquis de La Fayette7 Twitchell, b. 1827, son of William6 & Betsey E., m. Lucinda (lnu), in 1854/44. They lived in Wisconsin. [my ancestor]
Moses Jr - Moses6 Mitchell, son of Moses5 Twitchell & Dorcas Dolley, m. Kesiah P. Morton 1831
Leaving the following for further research:
It looks to me like either Moses Sr. or William decided to have the name change. Every child William had by 1828 underwent the name change. His brother Moses Jr, his Mother and Father, are the only others identified. But perhaps it was Moses Sr.'s idea. I know Moses was a pensioner, and managed to still receive his Rev. War Pension. So he wasn't hiding from the Gov. The Mitchells in Maine are extremely abundant by this time. By becoming a Mitchell one could certainly blend in.