How To Add Addl But_Onclick Event For Tag Manager

I want to add an event to send the Product Name to GTM when someone adds a product to their cart.

I've created an add_to_cart.override.tpl file to my changes.

But I don't know how to modify the but_onclick

What I'm looking to add is

on_click (event: "Product Added To Cart: {$Product.product})

CORE ADD TO CART code:

{include file="buttons/button.tpl" but_id=$but_id but_text=$but_text|default:__("add_to_cart") but_name=$but_name but_onclick=$but_onclick but_href=$but_href but_target=$but_target but_role=$but_role|default:"text" but_meta="ty-btn__primary ty-btn__big ty-btn__add-to-cart cm-form-dialog-closer"}

For example, you can add event with the following code. In this case changes in the core files are not required

                $(document).on('click', 'button[type="submit"][name^="dispatch[checkout.add"]', function () {
                    $.ceEvent('one', 'ce.formajaxpost_' + $(this).parents('form').prop('name'), function () {
                        ... your code here...
                    });
                });