Entymology:

Quenya: 

Father-name:

Maiwënil (Gull-friend) was the name given to him by his father at birth for he was born upon a Teleri ship as the gulls above circled.

Amilessë:

Tirë-Itaehtelë (Watcher of Sparkling Spray) is the name bestowed upon him by his mother who noticed his fascination with running water as a young elf. Most of all was his love for fountains and the jeweled mist they would issue. 

Sindarin: 

Tir-Eithelmîr was the name he later adopted after the end of the second age and Battle of Alliance, it is merely a Sindarin adaptation of his name in Quenya for the ease of those he dwelt with in Imladris.It is a rough translation that means watcher of the jeweled spray.

History:

Coming to the hidden city of Gondolin in Beleriand in the first age, Tir-Eithelmîr was named for his love of the fountains. Roughly translating to he who watches the jewelled spray in Westron, he was originally named in quenya, Tirë-Ñaltaehtelë and still goes by that name within Aman and amongst the Calaquendi. 

Enamoured by the light reflecting through the fine spray of the fountains, he set out to recreate the natural wonder through jewel craft. He tinkered long for many years until he was renowned for his artwork, setting jewels for the noble houses of Gondolin. He developed a particular fondness for working with silver and diamonds and began to work closely with smiths from the House of Fountain, learning from them how to wield a blade with grace of flowing water.

By the time of the betrayal and subsequent fall of Gondolin, Eithelmîr had become an able fighter and joined the ranks of the House of Fountain in the defence of his beloved city under the charge of Lord Ecthelion and King Turgon. Standing in defence of the House the King, Tireithelëmîr witnessed the defeat of the Balrog, Gothmog at the hands of his Lord, Ecthelion who perished in the act. As he stood, crushed by the sacrifice of Ecthelion he noticed that only in the fountain's waters were the fires of Morgoth extinguished. 

Weakened with his grief for his fallen city and the slaying of his kin, Ethielmir embarked upon the journey westwards across the ocean to settle in Aman. Here he spend many thousands of years regaining his strength, empowered with inspiration from the fountains of Gondolin, Eithelmîr believed he could reflect that power through jewel craft. 

Working with metal smiths in Valinor, Eithelmîr prepared to return to Middle-Earth at the turning of the second age to lend his skill to Gil-Galad and his army as they fought against Sauron in the Battle of the Last Alliance. After a seven year siege, Sauron fell and the one ring passed into the hands of men. 

During the battle of Dagorlad, Eithelmîr was wounded when he was lifted high into the air in the crushing talons of a fellbeast before being released above the heads of the Last Alliance, crashing down hard upon their heads. Eithelmîr was taken, unconscious back to Imladris under the care of Lord Elrond and his healers and there he has remained until now.