var nameArray:Array = new Array("name 1", "name 2", "name 3", "name 4", "name 5");
function getName(){
var ranNum = random(nameArray.length);
var randomName = nameArray[ranNum];
}
someButton_btn.onPress = function(){
getName();
}

to:

var nameArray:Array = new Array("name 1", "name 2", "name 3", "name 4", "name 5");
function getName(){
var ranNum = random(nameArray.length);
var randomName = nameArray[ranNum];
someTextField_txt.text = randomName;
}
someButton_btn.onPress = function(){
getName();
}