I believe pronunciation in Irish names varies quite a bit from region to region, so I'm reluctant to consider those as the only standard pronunciations. You also have to consider how English is pronounced in
Ireland. an Irish English-speaker may actually pronounce
Kathleen and Caroll exactly like their Irish counterparts.
Like earthnut said, these spellings are
approximations; it would be almost impossible to reproduce the exact sound of these names using only English phonetics. For instance, the sound "kh" in
Caitlín doesn't really exist in English; "tch" is no more correct than "th".
Using the examples you gave, the anglicized versions
Kathleen and Caroll are probably influenced by the existing names
Katherine (
Katharina in Latin) and (the unrelated)
Carolus. Apart from pronunciation, aesthetics probably also plays a role when anglicizing a name. Whence
Neve, rather than Neeve, Neive, or Neev (which would all work in English).
Alexandrina, Annabella, Clementine, Charlotte, Emilienne, Florence, Frederica, Katharina, Mary (May), Maud, Penelope, Rosamund, Theodora (Teddy).
Aubrey, Axel, Benedict, Bertrand (Bertie), Cuthbert, Dashiell, Everard, John (Jack) Leopold (Leo), Magnus, Matthias, Maximilian (Max), Wilfred.