Strider's true name is Aragorn, son of Arathorn. He is the heir to Isildur, and also the heir to the throne of Gondor. The rightful King. Gondor's rule (while the Fellowship was at the council of Elrond.) was ruled by what is called a "steward." Boromir, son of Denethor's father is/was* a steward. But Aragorn, by blood and birth right, can take back the throne. Whether Aragorn will choose to do that remains hidden still.
*The reason I have written is/was is because I don't know if Denethor remains king by the end, or if Aragorn does accept the throne. That is why. It does not in any way spoil part of the last book. As I have said before, there will be NO spoilers on this website. Thank you for understandung.