Wikipedia has an article titled postanalytic philosophy with the names of Quine, Davidson, Putnam, and Rorty given as examples. But I have not seen the term used much at all lately, it appears to be obsolete. The same names are often listed under logical pragmatism, together with Wittgenstein, and, with more names added, like Kuhn, Feyerabend and the Stanford Disunity Mafia, under postpositivism. Of these only Kuhn, Feyerabend and Rorty can be said to represent the analytic version of postmodernism. For Rorty's "creative" medley of pragmatism and continental postmodernism, which he termed "neo-pragmatism" and sometimes characterized as "post-philosophy", see e.g. Have any philosophers applied the concept of “underdetermination” to non-scientific contexts? Zammito's book referenced their is a nice critical review of "analytic postmodernism".
Even according to Wikipedia, "the term "postanalytic philosophy" itself has been used in a vaguely descriptive sense and not in the sense of a concrete philosophical movement". The term probably derives from Rajchman and West edited 1985 volume Post-Analytic Philosophy, which was inspired by Rorty. But it is clear now that they spoke too soon. "Postanalytic" philosophers are still commonly described as just analytic, and soon after the volume came out another major change came, the end of the linguistic turn, or at least the beginning of the end.
Language came to be seen as a disappointment as the master key to all philosophical mysteries, the first philosophy, and this downgraded the status of the initial insight of analytic philosophy derived from Frege and Russell, analysis of language. According to Burge, the focus shifted to philosophy of mind, the next "first philosophy". It would make more sense to call post-linguistic turn analytic philosophers "postanalytic", see Is it thought that analytic philosophy is in decline after the linguistic turn? (no).