Based on the work of Barry Griffin, the list below shows the five most popular surnames in Ireland and in each county in 1901.
Overall in Ireland
Murphy, Kelly, Walsh, Ryan and Sullivan
Connaught
Galway Kelly, Walsh, Burke, Conneely and Joyce
Leitrim Macgowan, Reynolds, Rooney, Flynn and Kelly
Mayo Walsh, Gallagher, Kelly, Moran and Murphy
Roscommon Kelly, Beirne, Macdermott, Brennan and Flanagan
Sligo Brennan, Gallagher, Walsh, Kelly and MacDonagh
Leinster
Carlow Byrne, Murphy, Doyle, Nolan and Kelly
Dublin Murphy, Kelly, Walsh Byrne and O’Brien
Kildare Kelly, Byrne, Dunne, Murphy and Doyle
Kilkenny Walsh, Murphy, Brennan, Ryan and Phelan
Laois Dunne, Phelan, Fitzpatrick, Delaney and Whelan
Longford Reilly, Farrell, Kiernan, Brady and Kelly
Louth Murphy, Byrne, Kelly, Carroll and Duffy
Meath Reilly, Lynch, Smith, Smyth and Farrelly
Offaly Kelly, Dunne, Egan, Daly and Carroll
Westmeath Kelly, Murray, Farrell, Daly and Reilly
Wexford Murphy, Doyle, Byrne, Walsh and Furlong
Wicklow Byrne, Doyle, Murphy, Kelly and Kavanagh
Munster
Clare Macmahon, Macnamara, O’Brien, Kelly and Moloney
Cork Murphy, Sullivan, Maccarthy, Donovan and Walsh
Kerry Sullivan, Shea, O’Connor, Connor and Murphy
Limerick Ryan, O’Brien, FitzGerald, Hayes and OConnor
Tipperary Ryan, Maher, Dwyer, Kennedy and O’Brien
Waterford Power, Walsh, Flynn, Murphy and Macgrath
Ulster
Antrim Wilson, Johnston, Thompson, Campbell and Smyth
Armagh Murphy, Hughes, Wilson, Maccann, Kelly
Cavan Reilly, Brady, Smith, Macgovern and Lynch.
Derry Doherty, Maclaughlin, Maccloskey, Kelly and Bradley
Donegal Gallagher, Doherty, O’Donnell, Boyle and Maclaughlin
Down Johnston, Thompson, Wilson, Martin and Brown
Fermanagh Maguire, Macmanus, Johnston, Armstrong and Gallagher
Monaghan Mackenna, Duffy, Connolly, Macmahon and Maccabe
Tyrone Quinn, Donnelly, Kelly, O’Neill and Devlin
Further information and a list of the top 100 surnames in each county in 1901 can be seen at this link:
https://www.barrygriffin.com/surname-maps/irish-tops/Ireland/1901
Barry also prepared maps depicting the prevalence of surnames in an area based on census data. The maps at this link https://www.barrygriffin.com/surname-maps/irish/ will show the locations where surnames occurred in 1901 and 1911. These maps are based on the 1901 and 1911 census data. While not being definitive on the occurrence of a surname, they do give an indication of the popularity of a given name in a specific area.