The story
Coined by American computer scientist and mathematician Donald Knuth in his novelette Surreal Numbers: How Two Ex-Students Turned on to Pure Mathematics and Found Total Happiness (1974). The concept had been developed by British mathematician John Conway for his game theoretic research of the board game go. Conway had simply called them numbers, but subsequently adopted Knuth's term and used it in his book On Numbers and Games (1976).
Etymology from Wiktionary, CC BY-SA 4.0.