I started with a primary source, the "Sufferings" of the Quakers in Moate Monthly Meeting — and immediately ran into the great dilemma of this type of research: who was Irish and who was English? Centuries of English colonization or "plantations" (preceded by Viking and Norman settlements), along with intermarriage, left a mixed populace. The question of whether a man was Irish or English might be restated as: "Which generation of English was he?"
The prefixes O' and Mac served as a guide as I scanned the indices of my reference books. MacLysaght also claims Crowe, Maloney, Brady, Cock and Spencer as Irish surnames. The best source for other surnames turned out to be The Grand Juries of County Westmeath, containing an appendix of family genealogies that takes up most of the book.
Given names for men
The most common are Daniel, Hugh, George, Edmond or Edmund, Sean, Thomas or Tom, and James. There were also several mentions of Torlogh or Turlough, Robert, Con or Conn, John, Eoin, Owen, Kevin, Brian or Bryan, Keadagh or Kedagh, Terence, and Donall, Donel, Donal.
More names: Denis, Fergal, Art, Redmond, Egan, Beare, Rory, Peadar, William, Michael, Ernie, Eamon or Eamonn, Dermot, Edward, Eddie, Antony, Anthony, Lucius, Jimmy, Cormac, Stephen, Henry, Raymond, Ramsey, Joe or Joseph, Martin, Frank, Art, Arthur, Seamus, Conor, Feagh, Charles, Cahir, High, Jeremiah, Patrick, Paddy, Colm, Allen, Neil, Neill, Shane, Abraham, Nial, Aghery, Christopher, Theobald, Nangle, Phelim, Mallachy, Maurice, Richard, George, Morgan, Conla, David, Hubert, Hume, Francis, Breasal, Thadeus, Garrett, Nathaniel, Peyton, Whitney, Francis, Logan, Theobald, Walter, Peter, and Cuthbert.
I primarily wanted early modern Ireland names, but Grand Juries also provides interesting ancient names with their Roman equivalents; you can see how they morphed into more modern names.
Duachus Galach, Duach, Errnin, Eogan (Owen), Fergusius, Feargna (Fergnaus), Achaius (Eochy Tiorm), Aodh Finn, Brenain, Cathalan, Arten, Orgaille (Orgallius), Brefny, Cu-Conachi (Constantine), Mac-nahighe or Macnahighe (Nicholaus), Tiernan, Godfrey (Godfridus), Maolsachlin (Mallachy), Giolla-Joso (Gelasius), Giola-Josa-Ruadh (Gelasius), Cathal (Cathaldus or Carolus), Donogh, Murketagh, Awly, Fergall, Andach, Morough, Matha (Mathew), Matthias, Rufus, Manus, Maolmordha, Philip, Cuconacht, Cormac, Mahon, Carbrey, and Fedlim (Phelim).
The names in Modern Ireland are more recent and possibly anglicized. They continue many of the names already listed, plus Justin, Connor, Frank, Oliver, Malcolm, Michael, Heber, Louis, Nevil, Samuel, Flann, Murrough, Mairtin, Feargus, Tomas, Cahir, Jeremiah, Sylvester, Ernest, and Philip.
Given names for women
By far, the most common name I found was Katharine, Catherine, Kate. Mary and Mary Anne also showed up several times.
Other names were Maud, Bernadette, Patricia, Rossa, Patsy, Nuala, Grace, Kitty, Dorcas, Genet, Margaret, Jane, Elizabeth, Susannah, Diana, Louisa, Ruth, Jane, Eleanor, Bridget, Sarah, Margaret, and Anne.
More ancient: Fedelonia, Indearva, Ranalt, Winifred, and Finguola (Penelope).
More modern (in addition to the names above, still in use): Deidre.
You'll notice I included nicknames and spelling variants. Here's a great resource on nicknames and how some names changed.