If we consider the Whitworth Institute, on the corner of the A6 and Station Road as the centre of the ancient parish of Darley, it would have included the settlements of Wensley and Snitterton to the south-west, Little Rowsley, Tinkersley, Northwood, Darley Hillside and Two Dales to the north, and Farley and Upper Hackney to the south-east. Wensley and Snitterton became a separate parish in 1840, becoming known as South Darley, whilst the remainder of the old parish retained its name as Darley for some years after that, though it was also recorded in some sources as 'North Darley'. The River Derwent marks the boundary between the two. The railroads often listed parish names with unique suffixes or prefixes on their time-tables, so that passengers could be more certain of where they were arriving. There are many places in England with the same names. These additiions often "stuck".
The emergence of the name “Darley Dale” in preference could be a consequence of the coming of the railway, and the renaming of the station at Darley to “Darley Dale” in 1890. Such an attraction as a 'Dale' would have captured the imagination of the Victorians, suggesting they could expect to enjoy some romantic scenery along the valley of the River Derwent, which the railway line follows north towards Bakewell.
Alternatively, it might have been deemed expedient with the coming of the postal service, to distinguish it from the parish of Darley Abbey in the south of the county, though it is not known when this 'shift' actually occurred. If the difference in Kelly's Directory of 1895 and 1912 can account for it, it would appear to have been some time between 1895, and 1912, as 'Darley Dale' was not mentioned in 1895.
Coincidentally - or otherwise the Whitworth Institute was opened the same year as the station was renamed - in 1890, 3 years after Sir Joseph Whitworth's death.
The settlement of 'Two Dales' is usually found in old documents referred to as 'Toad Hole'. It is not known when this changed, nor why, though I think most of us can have a good guess!