He was actually born Yngve johan malmsteen (a common name here in sweden), wich is pronouced a bit differently!
But when he moved to the us he changed his name, or more correct, the pronoucation of his name!
But now he only wants to be called "ingvay", I have actually heard of a guy at a pressconference that called him yngwie(pronouced the swedish way), and that yngwie got so mad he left directly, without taking any more questions! =)