var attr = $(this).attr('name');

// For some browsers, `attr` is undefined; for others, `attr` is false. Check for both.
if (typeof attr !== typeof undefined && attr !== false) {
  // Element has this attribute
}

$(this)[0].hasAttribute("name");

jQObject[0].hasAttribute("name");

$(this).is('[name]');

$(this).filter("[name='choice']");