Astronomers and astrophysicists have worked very hard in the last decade to discover ways of finding and characterizing extra-solar (from outer of our solar system) planets, because it's a very difficult task. The primary problem is that unlike stars, planets don't give off light-- and light is the primary means we have of investigating the universe. To discover them, scientists have to very carefully observe the light from stars-- if a planet is orbiting a star, very small changes in the way the light comes from the star will be observed over time. The gravity of the planet causes a number of effects, such as slowing the rotation of the star, or bending the light produced by the star (an effect called gravitational lensing). Because these techniques depend on the mass of the planet, most of the discovered planets are likely large gas giants, like our Jupiter or Saturn.

Because some of these methods give more conclusive and definite proof than others, there's no single figure for how many extra-solar planets have been found. Estimates range from several dozen to over two hundred! What's more, new ones are being discovered everyday. If you had to have an answer, I'd say over 100 planets outside the solar system are known for sure. As to their names? The people who discovered them have to assign them a technical name or number, and may have a personal nickname for them. But I don't think any have real, accepted names. Maybe as we get to know more about them, we'll see some of them named, too!

Some excellent resources are linked below:

Interactive Extra-solar Planets Catalog

exoplanet

Masses and Orbital Characteristics of Extra solar Planets

exoplanets

NASA Planet Quest

planetquest