Its a Yucca, specifically Yucca filamentosa. The yellow middle of the leaf suggests the variety 'Colour Guard'. That old flower spike means that it will produce new "daughter" rosettes or plants around the main one in the centre which will gradually die away.

American spelling of Colour (Color Guard) as it will have been named and registered in the USA.

Um, Fractal, looks more like Yucca flaccida 'Golden Sword' to me - I grow these in my garden. Gleedie, if the leaves have festoons of whispy threads or filaments hanging and curling off them, then its the one Fractal suggested - if none, or very few of those, then its Yucca flaccida.

Yes, could be that?

It looks more like Yucca flaccida to me, too, Gleedie. The acid test: Y. filamentosa normally loses all of its leaves in the winter; Y. flaccida is usually evergreen, but may lose it's leaves in exceptionally cold winters. I would remove the old flower stem as close to the base as possible, without damaging the leaves.