Sure. Anyone can call themselves a "public radio" station. They just can't put the word "national" in front of it, "international" after it, or "american" and "media" around it...lest they violate copyright by stating they are a NPR, PRI or APM (respectively) member station if they're not actually a dues-paying member station.
You don't even need to be a non-commercial station to call yourself a "public radio" station. You can brand yourself however you want, although if you're calling yourself a "public radio" station but your programming is not what "public radio" fans would expect, it's probably just going to backfire on you.