Amrod's father name in Quenya is Telufinwë, "Last Finwë", for he was the last of Fëanor's sons. His mother name was originally Ambarussa ("top-russet", referring to his hair), the same as his brother Amras, but Fëanor insisted that the twins ought to have different names and Nerdanel later called him Umbarto, "the Fated". His father, disturbed by it, changed it to Ambarto. Nevertheless both twins called each other Ambarussa.
However "Umbarto" proved to be a prophetic name, for Amrod was accidentally killed in the swan ships of the Teleri, when his father ordered them to be burnt at Losgar.
There is no trace of the death of Amrod at Losgar in the published The Silmarillion, as it was a very late idea by Tolkien, omitted by Christopher Tolkien as he did not at the time see how it could be incorporated into the primary text of The Silmarillion. Where both Amrod and Amras are mentioned in the published text after the landing in Losgar, it should according to Tolkien's later wishes be Amras alone. The information regarding Amrod's naming, especially, comes from The Peoples of Middle-earth. Amrod is the Sindarin version of the name Ambarto.
In The Silmarillion, Amrod is always found alongside Amras. Surviving the burning of the ships at Losgar, he and Amras lived as vassals of their brother Maedhros at an unspecified location in the forests of East Beleriand, and others of the Elf-lords would visit their lands from time to time. Amrod was wounded in the Nírnaeth Arnoediad, and later joined his brothers in the attack on Dior and the final destruction of Doriath, and then in the assault on the Mouths of Sirion. In this last battle, he and Amras were both killed.
^Martinez, Michael (31 August 2001). "It's all in the family: The Finweans". MERP.com Middle-earth Role Playing Community. Retrieved 6 October 2012. "The Shibboleth says their father-names (given in Quenya) were Nelyafinwe ("Finwe Third", as in Finwe III, Finwe the Third), Kanafinwe, Kurufinwe (spelled Curufinwe in The Silmarillion), Morifinwe, Pityafinwe ("Little Finwe"), and Telufinwe ("Last Finwe"). Maedhros is said to be the most handsome of the sons, and Curufin was their father's favorite because he was most like Feanor in spirit and skill. Curufin also resembled his father more closely than the other sons. Their mother-names were Maitimo, Makalaure, Tyelkormo, Atarinke ("Little Father"), Carnistir ("Red Faced"), Ambarusso and Ambarusso. The two Ambarussos were twins and Feanor asked Nerdanel to give one of them a different name. She chose Umbarto ("Fated"), which Feanor changed to Ambarto ("Exalted"), and he gave that name to the youngest."
^"...In the morning [after the burning of the ships] the host was mustered, but of Fëanor’s seven sons only six were to be found. Then Ambarussa went pale with fear. ‘Did you not then rouse Ambarussa my brother (whom you called Ambarto)?’ he said. ‘He would not come ashore to sleep (he said) in discomfort.’ But it is thought (and no doubt Fëanor guessed this also) that it was in the mind of Ambarto to sail his ship back [afterwards] and rejoin Nerdanel; for he had been much [shocked] by the deed of his father." (Tolkien, J. R. R. (1996), Christopher Tolkien, ed., The Peoples of Middle-earth, Boston: Houghton Mifflin, "The Shibboleth of Fëanor", ISBN 0-395-82760-4).
^Vinyar Tengwar 41. From the Shibboleth of Fëanor: "Had Amros (2) Ambarto lived, it [i.e. the name Ambarto] would probably have been [Sindarized] as Amrod."