gistfile1.js

var urlBase = "stuff";
var names = ['blah', 'blah', 'blah', 'blah', 'blah'];

// This will add the URL to your names, making them proper Twitch URLs.
_.map(names, function(name) {
    return urlBase + name;
});

// We need an empty array here to hold the data we're getting from Twitch.
var responses = [];

// Now, we iterate over the array (which are now URLs, not names), and do ajax stuff
_.each(names, function(url) {
    $.getJSON(url, function(theResponse) {
    
        // This takes our responses array and adds each response to the array as it comes in.
        responses.push(theResponse);
      
    });
});

/* 
    Now, what I would suggest at this point is that you start building DOM elements dynamically instead of doing it how you were.
    
    I would have an empty <div> in you document with an ID that you can use like #twitch or something to base the DOM on.
    
    Both ways would probably work, but I'd imagine this would be better.  You can do something like this...

*/

_.each(responses, function(data) {

    // Check to see if the stream is online, etc.
    if (data.stream) {
        var stream = data.stream;
        var streamdiv = $("#twitch").append("<div class='twitchuser'></div>");
        streamdiv.append("<h2>" + stream.display_name + "</h2>");
    } else {
        $("#twitch").append("<h2>Stream Offline</h2>")
    }
    
});

// In theory, the above code should dynamically build a div per person, and add a <h2> with the display_name from their JSON object.
// If this shit is broken, I can try to fix it tomorrow, I'm sorta tired, but this should get you started.
// You'll want to use streamdiv.append to create HTML elements and that's sort of how it works. Look at the following:
// http://api.jquery.com/append/