I don't think Gollum knew Bilbo's first name... I could be wrong but didn't he introduce himself in the Hobbit as Mr. Baggins?
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The seasons fall like silver swords, the years rush ever onward; and soon I sail, to leave this world, these lands where I have wander'd. O Elbereth! O Queen who dwells beyond the Western Seas, spare me yet a little time 'ere white ships come for me!
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