You're right, it does sound weird when Pippin starts acting all Gollumy. I think it's so that there's no doubt that he's talking about the Ring, without mentioning it specifically. He's trying to be sneaky, playing games with Grishnakh, and doesn't want to just come straight out with it.
Maybe it's possible that Grishnakh was one of Gollum's torturers, or that he had a spy or a mate who was.
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But Gwindor answered: 'The doom lies in yourself, not in your name'.
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