I don't think there's really a reason for the club being named ajax other than the fact that at the time this club was established it was the 'in' thing to name football clubs in the netherlands with greek methodlogy figures. We see this in the other clubs that use similar greek methology names such as Excelior and sparta in rotherdam, Heracles in Almelo, and a number of non-proffesional clubs such as Achilles 1894 of Assen.