What is the name of the magical school in 'The Magicians' trilogy?

The magical school in Lev Grossman's The Magicians trilogy is called Brakebills, formally Brakebills College for Magical Pedagogy. It is a secretive American institution where talented students are tested, trained, and taught the theory and practice of magic.

The protagonist, Quentin Coldwater, is admitted to Brakebills after an entrance examination. Although he expects something like the fantasy schools in the Fillory books he loves, Brakebills is more demanding and adult: students study disciplines such as transformation, physical magic, and spellwork, while dealing with rivalry, addiction, grief, and the consequences of real power.

Brakebills is not Hogwarts, Xavier's School, or Unseen University. Those schools belong to different fictional universes. Grossman's trilogy consists of The Magicians, The Magician King, and The Magician's Land, and Brakebills remains the central magical institution in the first book and an important setting across the series.