Arjuna was chiefly referred to, using ten appellations, in the Mahabharata epic.
These names along with their significance, was disclosed by Arjuna himself to Prince Uttara of the Matsya kingdom, before the war of Virata.
The ten appellations of Arjuna, along with the significance of each, are explained hereunder.
Arjuna said,
'I will, O son of Virata, tell thee my ten names.
Listen thou and compare them with what thou hadst heard before.
Listen to them with close attention and concentrated mind. They are Arjuna, Falguna, Jishnu, Kiritin, Swetavahana, Vibhatsu, Vijaya, Krishna, Savyasachin and Dhananjaya."
Uttara said,
Tell me truly why art thou called Vijaya, and why Swetavahana. Why art thou named Krishna and why Arjuna and Falguna and Jishnu and Kiritin and Vibhatsu, and for what art thou Dhananjaya and Savyasachin?
Arjuna said,
{1}They called me Dhananjaya because I lived in the midst of wealth, having subjugated all the countries and taking away their treasures.
{2}They called me Vijaya because when I go out to battle with invincible kings, I never return (from the field) without vanquishing them.
{3}I am called Swetavahana because when battling with the foe, white horses decked in golden armour are always yoked unto my car.
{4}They call me Falguna because I was born on the breast of the Himavat on a day when the constellation Uttara Falguna was on the ascendent.
{5}I am named Kiritin from a diadem, resplendent like the sun, having been placed of old on my head by Indra during my encounter with the powerful Danavas.
{6}I am known as Vibhatsu among gods and men, for my never having committed a detestable deed on the battle-field.
{7}And since both of my hands are capable of drawing the Gandiva, I am known as Savyasachin among gods and men.
{8}They call me Arjuna because my complexion is very rare within the four boundaries of the earth and because also my acts are always stainless.
{9}I am known among human beings and celestials by the name of Jishnu, because I am unapproachable
and incapable of being kept down, and a tamer of adversaries and son of the slayer of Paka.
{10}And Krishna, my tenth appellation, was given to me by my father out of affection towards his black-skinned boy of great purity.
Arjuna also had a few other names, as mentioned below.
{11} Gudakesha - someone who has control over sleep.
{12} Kapidhwaja - having flag of Kapi (monkey) in his chariot (Arjuna's flag displayed an image of Hanuman}.
{13} Parantapa - one who concentrates the most, destroyer of enemies from his concentration.
{14} Gandivadhanvan - one who possessed the mighty bow named 'Gandiva' which was created by Lord Brahma.
{15} Gandivadhara - Gandiva holder
{16} Madhyapandava - the third of Pandavas, younger to Yudhishtra and Bhima
and elder to Nakula and Sahadeva.
In addition to the above mentioned names, Lord Sri Krishna has addressed Arjuna with names
like-(i)Anagha-the sinless one(ii)Purushavyaghra-tiger amongst
men and (iii)Bharatasattama-best of the Bharatas, in the Srimad Bhagavad Gita.
Reference-Mahabharata Book:4, Virata Parva, Go-Harana Parva and Wikipedia