It's an Irish name - but some on that list are not. Grained, Movanna, Daria, Cushla and Macushla (though maybe in the US for those two).. I know several Mexican and Puerto Rican Carmelitas (mainly older women). Carmel is a Marian name used widely in Ireland in the past but not technically Irish.
Many Irish names that are now really popular were dug up and dusted off at the time of the Gaelic Revival. Some were taken from myth and legend, like Niamh, Maebh, Deirdre, Sorcha, Sile, Orla, Oisin, Conchubhair (Conor).
During the 18th-19th centuries names that were popular were introduced with the Normans, the Old English and subsequent groups who arrived - Jehanne/Joan/Jane, Mary, Margaret, Catherine, Anne, Elizabeth, Rose, Thomas, Michael, Gerard, Jeremiah, William, Daniel, Martin, John, James, Patrick, Dennis, Nicholas, Peter, Joseph, Edward, Paul. Some names became hybridised over the years - Rosaleen, Maureen, Kathleen, with the Irish diminutive added to the stem.
Names were registered in English (registers exist from the 1860s) - I think it is reasonable to suspect that there were official names and names used in everyday life, with Irish names used in Irish speaking areas and English versions used for interactions with the authorities including religious occasions (registration of various sacraments, marriages and burials) and for legal purposes. It is very possible that names like Siobhan, Sinead, Mairead, Caitlin/ Cait/ Caitriona, Eilis, Peadar, Seamus, Nora, Liam, Padraic, Tomas, and Micheal were used in daily life, along with names that you never hear any more, like Nabla, Bedelia (immortalised in the stories of Amelia Bedelia, the hapless Irish maid).
There were Irish saint names - Ita, Brigid, Ciaran, Colm, Senan, Iarlath, Canice, Colman, Eunan, Columba, Aidan, Feidhlim, Nathy, Muredach, Brendan, Macartan, Ciaran, Declan, Finbar, Fintan, Malachy, Nessan, Tadhg, Rory, Fiacre - some of these are the names of cathedrals, or strongly associated with certain areas.
Often children would be given one of these names as either a first or middle name or in the case of the patron saint of a diocese, they would be allowed to choose either Patrick, Mary, Brigid, or the diocesan patron as a Confirmation name. Often the names were Anglicised versions of Irish names. These ^^ are a mixture of Irish and Anglicised names.
Many of this sort of locally significant name was also dug up and dusted off at the time of the Gaelic Revival.
There were names popular in certain very small regions (I am familiar with names from certain baronies in Carlow and Wexford - examples include Anastatia, Judith, Moses, Moling, Laserian) with names like Honora, Julia, Celia, Delia, Fidelma, Philomena, Dymphna, Eleanor and Sarah/Sally/Sadie plentiful in many places. Then there were names like Attracta, Concepta, Dolores, and even the exotic Consuela. And names still found in Connemara and probably other Gaeltacht areas, like Briocain