The meaning of Aragorn is not clearly stated. A note found among J.R.R. Tolkien's papers at Marquette University suggests that "kingly valour" may have been the intended meaning.
Estel:
Elrond gave the name Estel to Aragorn when he accepted the boy as his foster son in 2933. The name means hope.
Chieftain of the Dunedain:
Aragorn became the Chieftain of the Dunedain on his father's death in 2933.
The Dunadan:
As Chieftain of the Dunedain, Aragorn was called the Dunadan by Bilbo and others at Rivendell. Dunadan means Man of the West, or Numenorean.
Isildur's Heir:
Aragorn was a direct descendant of Isildur, son of Elendil. Elendil was the last of the Lords of Andunie of Numenor and the first King of Gondor and Arnor.
About Aragorn
Aragorn was known as Strider, a Ranger who lived in the Wild protecting the people of Middle-earth. But he was descended from the ancient line of kings, and when he joined the quest of the Ring-bearer, the time came for him to fulfill his destiny. As Frodo Baggins struggled to reach Mount Doom, Aragorn fought the servants of the Enemy and revealed himself to Sauron as Isildur's Heir. After Sauron's downfall the Kingdoms of Gondor and Arnor were reunited under Aragorn's reign and peace and prosperity returned to Middle-earth.
Aragorn was a direct descendant of Isildur, son of Elendil. The Heirs of Isildur were the Kings of Arnor until that kingdom was divided in three in the year 861 of the Third Age. The line was then continued first by the Kings of Arthedain and then, when that kingdom was decimated by war and plague, by the Chieftains of the Dunedain.
Aragorn was born on March 1, 2931, and just two years later he became the sixteenth Chieftain of the Dunedain when his father Arathorn II was killed by Orcs. Aragorn's mother Gilraen took him to live in Rivendell, home of Elrond. Elrond accepted the child as a foster-son and gave him the name Estel, meaning "Hope." Aragorn was not told his true name and heritage until 2951, when he was twenty years old and Elrond perceived that he had grown to manhood. Elrond then gave Aragorn two of the heirlooms of the House of Isildur: the Ring of Barahir and the shards of Narsil.
The next day, Aragorn first met Arwen who had returned to Rivendell from Lothlorien to visit her father Elrond. When Aragorn saw Arwen he called her Tinuviel, for her beauty was reminiscent of Luthien Tinuviel, an Elf who gave up her immortality for the love of Beren, a Mortal Man. Aragorn fell in love with Arwen, but Elrond said that if she chose to be with Aragorn she would relinquish her immortality as Luthien had and that his daughter's age and experience as well as her lineage placed her too far above Aragorn. He told Aragorn that many years of trial lay before him.
The Sword That Was Broken
Thorongil:
Thorongil is the name given to Aragorn by the Men of Gondor while he was in the service of Ecthelion II.
Strider:
Strider was the name that Aragorn was known by in Bree.
Elessar:
Aragorn took the name Elessar when he was crowned King of Gondor and Arnor. The name referred to the green stone set in an eagle-shaped brooch that was given to Aragorn by Galadriel when he left Lothlorien.
Telcontar:
Telcontar was the name chosen by Aragorn for his royal house. Telcontar is the Quenya equivalent of "Strider".
Arwen Evenstar & Aragorn Elessar
At Rivendell, Aragorn was reunited with Arwen. Narsil was reforged by the Elvish smiths and Aragorn named it Anduril, the Flame of the West.