It wasn't a pendant, it was a brooch.
"Then she lifted from her lap a great stone of clear green, set in a silver brooch that was wrought in the likeness of an eagle with outspread wings; and as she held it up the gem flashed like the sun shining through the leaves of spring. 'This stone I gave to Celebrian my daughter, and she to hers; and now it comes to you as a token of hope. In this hour take the name that was foretold for you, Elessar, the Elfstone of the house of Elendil!'"
So yes, in a way Arwen's brooch was Aragorn's "namesake". This wasn't included in the movie, but they instead chose to feature the Evenstar. Maybe this is a good thing- if Aragorn had had another name in the movie, it would have been confusing. Yes, Thorongil is Aragorn.
What's interesting about the passage above is that it includes hidden references to Aragorn through his other names.
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an eagle with outspread wings
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Aragorn's other name, Thorongil, means 'Eagle of the Star.'
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the gem flashed like the sun shining through the leaves
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Isn't the sun a star? So you have an eagle reference and a star reference with the brooch. Incidentally, one of the other tokens of Aragorn's house was the Elendilmir, or the Star of Elendil... but I digress.
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now it comes to you as a token of hope
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Aragorn's name as Elrond's foster son was Estel. Estel is elvish for 'hope'.
Interesting, no? (Just say yes!
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