[SalesForce] How to get the current profile name in an aura cmp

init handler is called long before DOM is rendered in the view by the component. The appropriate place to access DOM, is in Renderer.

Add afterRender method which in turn gets called once the DOM rendering is done:

    afterRender : function(cmp,helper){
        this.superAfterRender();
        var elements = document.getElementsByClassName("myTest");
        console.log("elements.length: " + elements.length);
        for (var i=0; i<elements.length; i++) {
            console.log(elements[i].innerHTML);
        }
    }

I think what I would recommend here is to create nested components. So you have a parent component that will call the component you want to call here, and you can pass in attributes to the component. You technically will end up with 4 components, but the one is reused. So for example:

<aura:component >
    <aura:attribute name="specificParameter" type="String" required="true" />

    <div>
        {!v.specificParameter} is passed from the parent.
    </div>
</aura:component>

and in your parent component that is the quick action, you call your main component (ChildComponent) with the specific parameters you need.

<aura:component implements="force:lightningQuickAction" >
    <c:ChildComponent specificParameter="Test 1" />
</aura:component>