This is the Books' forum, right? In TTT, Theoden did not recognize Aragorn as Thorongil, assuming that anyone who had served under his father was either dead or very old. As for Denethor, that's in Appendix A, IV: "Gondor and the Heirs of Anarion"
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At the time many thought that Thorongil had departed before his rival became his master; though indeed Thorongil had never himself vied with Denethor, nor held himself higher than the sevant of his father
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Denethor knew that Aragorn was coming to Gondor because he had seen it in the Palantir of Anarion.