It's a Hedychium - a Ginger lily. Aren't you lucky to have it thriving in your garden! They're not always so accommodating. :-)))

Wow that is an interesting flower, I like it.

You are taking care of it the right way. You can chop off the old bits since it flowers on new rhizomes. If it was warmer where you are, it would spread rapidly. The Azorians call it Old Lady because the scent reminds them of old ladies. They also use the leaves in traditional bread baking.