Of the many ornate roman typefaces of the late 19th century, Dado is unusual in that it has a horizontal (or reversed) stress axis. It appears in MacKellar, Smiths & Jordan’s 1885 catalog (below) where it is shown as patented in 1882. The designer is assumed to be Herman Ihlenberg, as it is for so many of these MS&J faces.
The name is quite appropriate if it references the architectural terms for the lower part of a wall and the rail/molding that divides it. The heavy stroke at the face’s x-height forms something of a dado rail along a line of letters.