Your question really comprises of two parts, as you don't necessarily have to make your functions anonymous if they are assigned to a variable or property.
Named vs anonymous?
@Raynos highlights the main points clearly. The best part about named functions is that they will show themselves in a stack trace. Even in situations where functions are being assigned to variables/properties, it's a good idea to give your functions a name just to aid with debugging, however I wouldn't say anonymous functions are evil at all. They do serve a fine purpose:
Are anonymous functions a bad practice in JavaScript?
Function declaration vs function expression?
For that part of the question I would refer you to this question as it probably covers the topic in far more depth than I can
var functionName = function() {} vs function functionName() {}
