Okay, so naming customs among the elves are a little more complicated that most readers would probably prefer. This is mostly because Tolkien, being a linguist and all, took every opportunity to create a new name/word. So (especially in the Silmarillion) we see most of the Noldor having several names. Some of this is just because when the Noldor came to Middle Earth they had to “Sindarize” their names after Thingol’s ban on Quenya. So, for example, Galadriel’s Quenya name is Artanis ((EDIT: Her father-name was Artanis, but Celeborn called her Alatariel. Since the Sindarized version of Alatariel was prettier, she used that instead of Artanis. So Galadriel is the Sindarized version of Alatariel.)) Tolkien generally uses the Sindarin names as default, so those are the ones that will be most familiar to you. The Noldor generally chose their preferred names to be Sindarized, and left the others in Quenya form.
Aside from the Sindarin names, among the Noldor it was customary for a person to have a few names to begin with. When an elf was born, the father would give the child its first name (thus it was called the father-name.) In the early Age, the father-name was usually a variation of the father’s own name, and if the child was a girl it was usually a variation of the mother’s name. Sometimes (more often in the early Ages) a child would also receive a mother-name, sometimes called “names of insight” since they usually had something to do with the child’s fate. The mother-name tended to be more widely used than the father-name, since it wasn’t so similar to the father’s own name.
Finally, the Noldor had a ceremony ( usually between ages 7 and 10, but really whenever the child was considered capable of taking “pleasure in the sounds and forms of words” - the Noldor really liked their language) where the child would give themself their own name. This name was usually inspired by the child’s personal characteristic - a mark of individuality. This name was more private, and was usually only used among family and close friends and probably wouldn’t be widely known. Also, on top of all this, sometimes elves would have “after-names” which were earned later in life, which was more of a nickname/title of honor.
When trying to find everybody’s different names, it’s generally most efficient to search them on Tolkien Gateway. Each character’s page has an Etymology section, which lists their different names and what they mean. But here I’ll list the names of Feanor and his sons, just as an example:
Amras: Telufinwe, Ambarussa (Feanor demanded that Amrod and Amras have different mother-names, so Nerdanel changed it to Umbarto (“the Fated”), but Feanor thought it was unsettling so it was changed againt to Ambarto, but the twins just called each other Ambarussa)
This was the intensely simplified explanation of this topic. Again, being the language-lover that he was, Tolkien wrote about Noldorin naming customs a lot, so if you have another question on the subject, let me know. But, as far as finding everybody’s different names, Tolkien Gateway is really your best bet.
SOURCES: History of Middle Earth vol. 10 (“Laws and Customs Among the Eldar”), and vol. 12 (“The Shibboleth of Feanor”)
