For all reasonable sizes of black holes, the flux due to Hawking radiation would be _so ridiculously low_ that it wouldn't change anything about our usage of the term "dark matter".
In fact most dark matter models do assume some form of extremely weak interactions with normal matter or dark matter decay, which is how we try to detect dark matter. The effective flux from such interactions is a lot larger than Hawking radiation would be.
In fact most dark matter models do assume some form of extremely weak interactions with normal matter or dark matter decay, which is how we try to detect dark matter. The effective flux from such interactions is a lot larger than Hawking radiation would be.