The problem is likely that the "hide" function takes a second to hide things, so it's not actually hidden yet when you check if it's hidden. One way to solve that would be to check if it's hidden after the hide operation. That would go something like this:
$(document).ready (function() {
$("#image").click(function() {
$("#image, #name").hide("slow", function() {
if ($("#image").is(":hidden")) {
alert("Ok");
};
});
});
});
If you want to know more about the options you can use with the hide function, look here:
http://api.jquery.com/hide/