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I don't think it's going to matter one way or another to the company. The listing was either put up by an agency, or by some low-level HR assistant, and either way the decision-maker who actually looks at your resume is going to simply assume the company name was in the listing, they'll never even consider the possibility that you were all clever in finding it among all the other generic instances in the listing.
On the other hand, if there is even the slightest chance that you will ever use this cover letter as a template for another application, by including a company name you will be setting yourself up for a real screwup by accidentall leaving the wrong company in the letter. I say generic is safer.
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