This map shows the 1881 distribution of Greenhalgh by county. Almost all are in Lancashire (5631) with Yorkshire (131) and Cheshire (152) trailing behind. But the map distorts the data as it does not show the distribution within the county. One person in Aberdeenshire is enough to shade the whole of that county.
The map below shows that 3361 of Lancashire's 5631 are in Bury and Bolton areas (although note that areas on this map represent poor law unions). The 9 areas contiguous with Bolton and Bury bring the total up to about 4700 or about 84%. From this it will be clear that the name is as unusual in parts of Lancashire as it is in many other counties. Some areas of the lower map are in Cheshire (eg Stockport) or Yorkshire (eg Halifax).
Both maps were prepared with Surname Atlas from Archer Software