I'm not sure if you want all white spaces removed or to have words separated by 1 space. Below are 2 examples. And yes, I don't like RegEx, but was doing something similar the other day.
An example with no white space.
var name = "this is the test case";
name = name.replace(/\s/g, '');
document.getElementById("test1").innerHTML = name;
An example with 1 space between words.
var name = "this is the test case";
name = name.replace(/\s+/g, ' ').trim();
document.getElementById("test2").innerHTML = name;
Test in HTML.
<div id="test1"></div>
<div id="test2"></div>