Jim,
You gotta make sure the limit for the second loop is the starting point plus the length of your name.
/*jshint multistr:true */
var text = "Hey, how are you \
doing? My name is Joshua Stoutenburg.";
var myName = 'Joshua Stoutenburg';
var hits = [];
for (var i = 0; i < text.length; i++) {
if (text[i] === myName[0]) {
for (var j = i; j < i + myName.length; j++) {
hits.push(text[j]);
}
}
}