Don't use eval unless you absolutely, positively have no other choice.

As has been mentioned, using something like this would be the best way to do it:

window["functionName"](arguments);

That, however, will not work with a namespace'd function:

window["My.Namespace.functionName"](arguments); // fail

This is how you would do that:

window["My"]["Namespace"]["functionName"](arguments); // succeeds

In order to make that easier and provide some flexibility, here is a convenience function:

function executeFunctionByName(functionName, context /*, args */) {
  var args = Array.prototype.slice.call(arguments, 2);
  var namespaces = functionName.split(".");
  var func = namespaces.pop();
  for(var i = 0; i < namespaces.length; i++) {
    context = context[namespaces[i]];
  }
  return context[func].apply(context, args);
}

You would call it like so:

executeFunctionByName("My.Namespace.functionName", window, arguments);

Note, you can pass in whatever context you want, so this would do the same as above:

executeFunctionByName("Namespace.functionName", My, arguments);