This is from the Encyclopaedia of Arda:
Quote:
'The Eagle of the Star', an alias taken by Aragorn in his youth, when he journeyed to Rohan and Gondor and performed services to their lords.
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Why he chose the name and what it is actually referring to is up for debate, I guess. Personally, I think he chose the name because it was in line with the Elven names used in Numenor before they became obsessed with mortality. Thus, a reference to Numenor (his past and essentially future) and somewhat ironic and tongue-in-cheek as he used it in Minas Tirith with the Steward, considering he would eventually replace the position!
The complicated and rather mythical meaning which was in all likelihood known to few, was probably also good for his mysterious persona; a wise man (metaphorically from the West) who did great things and asked for nothing, and revealed little about himself.