Those are the formatting options available in ArcGIS.com when configuring popups. If you are using the popup in an application built with the ArcGIS API for JavaScript you could apply a custom formatter for your date info by using the InfoTemplate to define the popup content instead of the PopupTemplate. The InfoTemplate has lots of formatting options including the ability to define a date pattern of your choice:
var popupTemplate = new esri.InfoTemplate("Test","Date: ${datetime:DateFormat(datePattern: 'h \\'o\\'\\'clock\\' a, zzzz', selector: 'date')} Magnitude: ${magnitude}");
//create a feature layer based on the feature collection
var featureLayer = new esri.layers.FeatureLayer("http://sampleserver3.arcgisonline.com/ArcGIS/rest/services/Earthquakes/EarthquakesFromLastSevenDays/MapServer/0", {
mode: esri.layers.FeatureLayer.MODE_ONDEMAND,
infoTemplate: popupTemplate,
outFields: ['datetime','magnitude']
});