The correct syntax is :
$().SPServices({
operation: "GetUserLinks",
accountName:"username",
completefunc: function (xData, Status) {
console.log(xData)
}
});
Your syntax for the SPGetCurrentUser is correct but that doesn't on my Sharepoint... I see, at least, two other options to find the current user :
With SharepointPlus (a JavaScript API) :
$SP().whoami({url:"http://my.si.te/subdir/"}, function(people) { console.log(people["AccountName"]); });
Or you can change your masterpage to always have the details regarding the current user into your code. Have a look at this English blog post or this French blog post. Then it's easy to get the username from the HTML directly.