|Meaning:||1. Brittonic dol ‘haugh, holm’|
|2. Brittonic dol ‘church-land‘|
|3. Gaelic dail ‘haugh, holm’|
|4. Scots dale ‘share, portion’|
The place-name pre-fix dal- is common in the parish of New Cumnock and is present in a number of place-names including Dalhanna, Dalleagles, Dalgig and Dalricket.
Professor W. J. Watson in “The Celtic Place-Names of Scotland”  explains –
In Wales, Cornwall and Britanny, the term dol ‘meadow, dale, valley’ is common in names of places. In Scotland it was also common, appearing in the older forms of our place-names as Dol, Dul later Dal. In Gaelic pronunciation of the present day, initial Dal is always dail in the west and usually in the east. As to distribution, Dal is very common in Ayrshire there being 83 names so beginning in the index to the Retours – the actual instances much more numerous.
Dol, Dul, is found bot uncommonly with the names of saints, indicating an old church or site or land gifted to the church.
The challenge is to determine if the first element of the New Cumnock dal- names is of Brittonic dol- or Gaelic dail-. It should also be noted that Scots holm ‘a stretch of low-lying land beside a river; a meadow’  is commonly used in the parish and found in both Dalleaglesholm and Dalhanna Holm in the parish, example of place-name tautology.
In the Old Statistical Account of the neighbouring parish of Old Cumnock the Reverend Thomas Miller  in describing the parish soil writes-
all the holms are of a light dry soil, formed of sand and gravel
Alan G. James  introduces an intriguing alternative for Brittonic dol- and suggests that in some cases “it might have been adopted specifically as a term for a piece of church land”.
Footnote : Courtesy of Alan G. James
Essentially, both Brittonic dol and Gaelic dail are ‘a haugh’, the latter probably adopted from the former. Scots dale ‘share, portion’ (< OE dāl, which may have been phonetically close to the Pictish form of dol) may have influenced the use of dail in that sense. The association with saints’ names seems to be restricted to Pictland, and suggests some particular ecclesiastical association in either Pictish or early Gaelic usage.
| Watson, William J., 1926, The History of the Celtic Place-names of Scotland (Edinburgh and London).|
| Dictionary of Scots Language | holm|
| Old Statistical Account Vol. VI (1793) | Old Cumnock|
| James, Alan G., 2013, “P-Celtic in Southern Scotland and Cumbria: a review of the place-name evidence for possible Pictish phonology”, The Journal of Scottish Name Studies, 7, 29-78.|
Anent dol/ dail/ dale, you should refer to Simon Taylor’s discussions of that complicated group of elements – most recently, in PNs of Kinross 2017, 657 and 659.