Simple. Declare the function before the handler.
var onPutMap = function(evt){
console.log("This is a Test");
}
$("#demoMapPut").click(onPutMap);
Now, let's mix in some best practices (and a touch of my OCD).
First, it is good to name your handlers based on what they handle. So not 'onPutMap' but 'onClickMapPut' would be better. Also, I recommend also using 'on' instead of the click shortcut. Also, it is good to always use single quotes for string declarations. So my OCD rewrite looks like this:
var onClickDemoMapPut;
onClickDemoMapPut = function ( event ) {
console.log( 'This is a test' );
}
$( '#demo-map-put' ).on( 'click', onClickDemoMapPut );
I know these are all simple, and maybe silly looking, but some can save a lot of time. For example, look at the handler name 'onClickDemoMapPut': convention tells me exactly what to call it. This helps reduce silly errors and cognitive overhead.
Also, there are x-browser issues surrounding mixed-case class and ID names. It is wise to use only lower case for these purposes. Also, the class name has dashes as a form of namespacing and avoiding mixed-case.
Cheers, and good luck!