He is Joel in the earlier censuses with his parents, but in other records he is Joseph W. Remington. The marriage record identifies his parents as Orsin Remington and Eliza Ham.
He was likely named after his uncle Joel Ham. His bravestgone has his name as Joel W. Remington.
Possibly he was called Joe and census takers and other record-keepers wrote down Joseph?
In 1900, the family is at West Jersey, Stark Co., IL; according to census data Joseph and Ella have been married 10 years.
In 1910 Joseph and Ella are living in Toulon, Stark Co., IL; married daughter Addie Ogburn and her husband Clarence are with them. Daughter Mabel Wilson and her husband Edward are next door, and they have a son Joel.