Essë is the Quenya word for "name", as well as the 31st tengwa letter. In Tolkien's legendarium, Elves are given three names in their lives, the father-name, the amilessë (mother-name) and the epessë (nickname or honorary title).
Elves were typically given two names at or near birth: a father-name, which often was based on the father's own name or (in later times) was derived from old legends, and a mother-name, which was held to be prophetic.
The epessë was the third type of name, and unlike the other two, it was given later in life, or chosen by the Elf himself. An Elf could be referred to by any of the three, but a self-chosen name typically took preference.