Source: Part 11 of The History of Ireland (BOOK I-II) by Geoffrey Keating.
In the first place, we shall set down every name that was at any time on Ireland.
The first name which was given to Ireland was Inis na bhfiodhbhadh, that is to say Island of the Woods; and the person who called that name to it was a warrior of the people of Nin, son of Bel, who came from him to spy out Ireland, and on his coming thither he found it to be all one forest-wood, except Magh-n-ealta alone. Three times, indeed, Ireland was one continuous wood, according to this old saying, which is in the ancient record : “Three times Eire put three coverings and three barenesses off her.” (p.99)
The second name was Críoch na bhfuineadhach from its being at the limit or end of the three divisions of the world which had then been discovered; fuin indeed, from the Latin word finis being equivalent to ‘end’.
The third name was Inis Ealga, that is, noble island; for inis and oiléan are equivalent, and likewise ealga and uasal: and it is during the time of the Firbolg it was usual to have that name on it.
The fourth name was Eire, and it is said that wherefore that name is called to it, according to a certain author, is from this word Aeria, which was an old name for the island which is now called Creta or Candia; and why that author thinks that is because the posterity of the Gaedheal glas dwelt in that island some space of time after Sru, son of Easru, son of Gaedheal, had been driven out of Egypt: and, moreover, Aere is given as a name for Egypt whence the Gael proceeded. However, it is the common opinion of antiquaries that why it is Eire is from the name of the queen of the Tuatha Dé Danann who was in the land a the time of the coming of the of the Clann Míleadh into it: Eire, daughter of Dealbhaoth, was her name, and it is she was wife to Mac Gréine who was called Ceathúr who was king of Ireland when the sons of Míleadh came to it.
The fifth name was Fódhla, from a queen of the Tuath Dé Danann, who was called Fódhla: it is she was wife to Mac Cécht, whose proper name was Teathúr.
The sixth name was Banbha, from a queen of the Tuatha (p.101) Dé Danann, that was in the land, who was called Banbha: it is she was wife to Mac Cuill, whose proper name was Eathúr. These three kings held the sovereignty of Ireland each year by turns; and it is the name of the wife of each one of them would be on the island the year he was himself king. It is why the island is called Eire oftener than Fódhla or Banbha, because that is the husband of the woman whose name was Eire was king the year the sons of Míleadh came there.
The seventh name was Inis Fail; and it is the Tuatha Dé Danann gave that name to it, from a stone they brought with them into it, which was called the Lia Fail: and Saxum fatale, i.e. ‘Stone of Destiny’, Hector Boece calls it in the history of Scotland; and it was a stone on which were enchantments, for it used to roar under the person who had the best right to obtain the sovereignty of Ireland at the time of the men of Ireland being in assembly at Tara to choose a king over them. However, it has not roared from the time of Conchubhar forward, for the false images of the world were silenced when Christ was born. Here is a verse of quotation proving that it is from this stone Ireland is called Inis Fail, as Cionaoth the poet said : –
1. The stone which is under my two heels,
from it is named Inisfail;
Between two shores of a mighty flood,
the plain of Fál on all Ireland.
The eighth name was Muicinis; and it is the children of Míleadh who gave it that name before they arrived in it. When, indeed, they had come to the mouth of Innbhear Sláinghe, which today is called the Haven of Lochgarman, the Tuatha Dé Danann, with their druids, assemble to oppose (p.103) them there, and they practise magic on them, so that the island was not visible to them but in the likeness of a pig, so it is, therefore, they gave (the name) Muicinis to Ireland.
The ninth name was Scotia; and it is the sons of Míleadh who gave that name to it, from their mother, whose name was Scota, daughter of Pharao Nectonibus; or it is why they called it Scotia, because that they are themselves the Scottish race from Scythia.
The tenth name was Hibernia; and it is the sons of Míleadh gave that name to it. However, it is said that it is from a river that is in Spain which is called Iberus (the name) Hibernia is given to it. It is said also that it is from Eibhear (Eber), son of Míleadh, it is called Hibernia; but, however, holy Cormac, son of Cuileannan, says, that why it is called Hibernia is from this compound Greek word ‘hiberoc’ (ie. occasus in Latin) and ‘nyaon’ (i.e. insula) that is equivalent to saying insula occidentalis, i.e. ‘western island’.
The eleventh name was Iuernia, according to Ptolemy, or Iuerna, according to Solinus, or Ierna according to Claudian, or Vernia according to Eustatius. I think there is no meaning in the difference which is between these authors concerning this word Hibernia, but that they did not understand whence came the word itself; and, accordingly, that each one of them separately gave a guess from himself at it, so that from that came this variation on the word.
The twelfth name was Irin, according to Diodorus Siculus.
The thirteenth name was Irlanda; and I think that the reason why that name was given to it is, because that (p.105) it was Ir, son of Míleadh, was the first man of the Clanna Míleadh who was buried under the soil of Ireland, and accordingly, the island was named from him: ‘Irlanda’ and ‘land of Ir’ being indeed equivalent, for ‘land’ in English, and ‘fonn’ or ‘fearann’ in Gaelic are alike. The truth of this thing is the more admissible, since the book of Armagh says that a name for this island is Ireo, that is to say, the grave of Ir, because that it is there is the sepulchre or grave of Ir.
The fourteenth name was Ogygia, according to Plutarch: indeed, ‘Ogygia’ in Greek and insula perantiqua, i.e. most ancient island, are equivalent; and that is a suitable name for Ireland, because that it is long since it was first inhabited, and that perfect is the sound information which its antiquaries possess on the transactions of their ancestors from the beginning of eras, one after another.
For information on other Irish names, such as for people, see this page.
Tristan and Iseult is a love story that a harper, or minstrel, tells at Camelot, the court of King Arthur. Tristan, nephew of King Marc of Cornwall, slays an Irish knight in a duel, thus averting a war. Later Tristan, shipwrecked in Ireland, kills a dragon that is scorching the countryside, and is forgiven for his victory over the Irish champion knight. He brings home the princess Iseult (Isolde, Isolt, Ysolt) to be the bride of King Marc in order to cement the peace between their two countries. But on the trip back to Cornwall, Tristan and Iseult fall passionately in love. Though Iseult becomes queen of Cornwall, the love affair continues until they are betrayed to King Marc. She is rescued from burning at the stake by Tristan wearing leper’s clothes, and they escape to live in the forest. In the end Marc forgives his queen and Tristan is banished. Then he comes to Arthur’s court and becomes a knight of the Round Table. When he dies, Iseult arrives too late to see him, and she dies of a broken heart. King Marc buries them together, and hazel and honeysuckle plants spring from the ground over their hearts and twine together over their grave. 
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