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Aragorn came from Gondor. Arathorn his father was king
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No. Aragorn was born in the north of middle earth in the former realm of Arnor. His father was never king, but was cheiftain of the dunedain of the north as was all his forefathers back to the time of the son of the last king of Arnor.
Aragorn had many names because he wanted to conceal his true identity and so took the various names given to him by others.
His importance was that he was the last remaining descendant of Elendil, the first king of Arnor and Gondor. The significance of him being descended through many fathers from Isildur, is that this made him eligible to claim the kingship of Gondor, as Isildur was a king of Gondor, and remained high king when he left to take up rule of Arnor. The fact that Aragorn was descended from Isildur meant that he had a rightful claim to the throne because Isildur's line should have kept the kingship of Gondor as well.
He doesn't claim the ring, despite the fact it was taken as an heirloom of his house by Isildur was because Aragorn understood that the ring was evil and could only really belong to Sauron. He knew that if he claimed the ring, it would destroy him and allow Sauron to become victorious.
I hope this is helpful.