A naked singularity means that you can see an infinitely dense thing. Black holes don't count because it sucks up all the light, so you won't see or otherwise detect it. But wait, if you are within the event horizon, would the black hole be a naked singularity from your view, since now you can see the infinitely dense center?
The event horizon isn't like a heavy cloud cover that you can "break through" and see clearly again on the other side. The event horizon actually isn't a physical thing at all, just like any other border isn't a real thing. If you're hiking through the Sahara you might pass from one country to another and not know it: there's no line drawn in the sand to mark the border. Likewise with a black hole, you don't notice when you're crossing the horizon because there's no immediate change in your surroundings.
Remember that the horizon is just a 'border' which marks where the escape velocity raises above luminal speed. As you fall into a black hole, light is still falling in on you from the outside universe, but closer to the singularity the escape velocity is even higher than where you are; so looking toward the singularity, you see the horizon retreating from you as you fall in - even after you've already crossed the horizon.
If you are falling into a Schwarzschild black hole you will never cross an event horizon. As you fall in you observe an apparent horizon that retreats before you as you fall inwards. The distance between you and the apparent horizon reduces as you fall, but it only goes to zero when you reach the singularity.
If you're interested to know more about this have a look at the questions Taking selfies while falling, would you be able to notice a horizon before hitting a singularity? and Would the inside of a black hole be like a giant mirror?.
So you will not observe a naked singularity at any point as you fall inwards.
I've restricted this to a Schwarzschild black hole because the charged and rotating black holes have the complication that there are two horizons and the singularity is timelike not spacelike, and an observer can fall in through the two horizons and back out of the black hole again. I don't know whether an observer could observe the singularity in these geomeries, but it seem possible that they could.
Basically what Asher said, and I love thought experiments like this, so I can't resist posting an answer too.
You couldn't see a singularity from inside the black hole for basically the same reason you can't see it from outside the black hole. No light from the singularity reaches you unless you're actually in the singularity, which probably wouldn't be much fun.
If you imagine yourself inside the event horizon of a black hole, everything inside the black hole is moving towards the singularity, nothing is coming from the singularity towards you, so all you can see is stuff that came from the universe falling into the black hole. Now, red shifts/blue shifts and curved space, anything you see would be hugely warped and much of it, spagetified and extremely difficult to recognize, but that's all you'd be able to see. No singularity. You might even be able to see the entire future of the universe, but still, you wouldn't see the singularity.
You might be able to see hawking radiation from inside the black hole (at least, I see no reason why you wouldn't) and that would likely increase in intensity as you approach the singularity, but what you observe wouldn't be the singularity but simply an effect on space by the singularity. Also, since a singularity is, in theory, smaller than an atom, I'm not sure what you'd expect to see anyway. :-)
If you want to get really creative about this, it might (I'm not sure), but might be possible to see a singularity in a Kerr black hole without going inside, but that's above my pay grade and I repeat. I'm not sure.