Semanticamente você está perguntando "insira concorrentes onde ainda não existe":
INSERT Competitors (cName)
SELECT DISTINCT Name
FROM CompResults cr
WHERE
NOT EXISTS (SELECT * FROM Competitors c
WHERE cr.Name = c.cName)
INSERT Competitors (cName)
SELECT DISTINCT Name
FROM CompResults cr
WHERE
NOT EXISTS (SELECT * FROM Competitors c
WHERE cr.Name = c.cName)