Aragorn takes the royal name Elessar after becoming king in J.R.R. Tolkien’s The Lord of the Rings.
The name Elessar means “Elfstone” in Quenya. Aragorn receives the Elessar jewel from Galadriel, and the name becomes closely connected with his kingship. After Sauron’s defeat, he is crowned King Elessar and rules the Reunited Kingdom, combining the realms of Arnor and Gondor.
Aragorn’s royal identity is also tied to his descent from Isildur and the kings of Númenor. Before openly claiming the throne, he travels under several names and identities, including Strider and Thorongil. His long period as a Ranger helps explain why other characters initially see him as a weathered wanderer rather than a king.
Telcontar is another name associated with Aragorn’s royal house: it is the Quenya form of “Strider” and becomes the name of his dynasty. That is why Elessar is the best answer for his personal regnal name, while Telcontar refers to the royal house.