No you have to take array of Color type not String type as following.
void Start() {
Color[] colors = {Color.green,Color.red, Color.white, Color.blue};
int lengthOfColors = colors.Length; //Isn't this is better name than thename?
int rndColor = UnityEngine.Random.Range (0, lengthOfColors);
gameObject.GetComponent<Renderer>().material.color = colors[rndColor]; //note the small 'c' in material.color
}