J.R.R. Tolkien gives Aragorn the name Elessar after his coronation.
Aragorn is crowned King Elessar after the defeat of Sauron and the restoration of the kingdoms of Gondor and Arnor. The name means “Elfstone” in Tolkien’s invented Elvish languages and connects Aragorn with the green jewel that becomes an important symbol of his kingship.
In The Lord of the Rings, Aragorn’s royal title is presented as Elessar Telcontar. “Telcontar” is a Quenya rendering of “Strider,” the name Aragorn used while travelling in disguise. His identity therefore preserves both his humble ranger past and his restored royal lineage.
Aragorn has several other names, including Strider, Estel, and Thorongil, which can make this question confusing. Isildur is one of his ancestors, not his coronation name. Elessar is specifically the title associated with Aragorn as king.