In T. H. White's The Once and Future King, the wizard who mentors Arthur is Merlyn. White deliberately uses this spelling to distinguish his version of the legendary magician from the more familiar modern spelling Merlin.
Arthur is known as the Wart during his childhood, when Merlyn begins educating him before he becomes king. Rather than relying only on lectures, Merlyn transforms the boy into different animals, including a fish, hawk, ant, goose, and badger. Each experience teaches Arthur about power, violence, cooperation, justice, and the consequences of leadership.
Merlyn is unusual because he lives through time backward: what is his past is often Arthur's future. This explains his strange knowledge and absent-minded behavior, while also allowing him to guide Arthur with an awareness of events still to come. His lessons shape Arthur's later attempt to replace brute force with a more just political order.
The character draws on older Arthurian traditions, but White gives him a larger role as teacher, political thinker, and moral guide. Dumbledore, Gandalf, and Obi-Wan are mentors in other fictional worlds, not in White's Arthurian retelling.