Have you managed to trace further back from Richards Father (John Wells-Garrett b.1804)?
I think he married Caroline Matilda Pask, was a shoe maker and had a number of children (Francis, Caroline, Richard, William, Elizabeth, James, Thomas, Susan and John).
His Son John being the eldest and apparently its a 'Garrett' thing that the eldest son is named after his father. Which has held true all through our branch.
I must confess I am not a Garrett by name, but my mother was, and tells me I'm the image of Garret Generation.