It wasn't a poet.

No single person is credited as the poet. The spoken word snippets on The Dark Side of the Moon are mostly recordings of random people answering questions in the studio. The most famous line (“I’m not frightened of dying…”) comes from Gerry O’Driscoll, the band’s Irish doorman. The closing line (“There is no dark side of the moon…”) is Peter Watts, a road manager. A few other voices belong to Paul McCartney’s wife Linda (uncredited) and studio staff. The band just asked a set of questions and took the best bits.

So it’s not poetry in the traditional sense – it’s found audio. The credits on the album list no individual poet, only “spoken word” as a general credit.