I recognized their names from the first example in the classic book "Algorithm Design" by Kleinberg and Tardos. But there it was called Gale-Shapley Algorithm.
The algorithm is due originally to Gale and Shapley, in a 1962 publication in the American Mathematical Monthly, but Gale isn't eligible due to the rule against posthumous awards. Roth is included because he was the first to apply it practically in economic-matching settings, quite a few years later.