Cohassett, AlabamaCohassett, also known as Lowell, is an unincorporated community in Conecuh County, Alabama, United States.HistoryCohassett is likely named for Cohasset, Massachusetts. A post office operated under the name Cohassett from 1880 to 1919. After that date the post office in Red Level handled the mail. However the original post office building is still standing.