Unfortunately there's no way to do a free reverse cell phone look up, the information is kept by the large cellular phone companies. They release the information but for a price.
Some private companies collect all this data from the various cell phone networks, sort it, and upload it to the net (no small feat). It's this convenience that we now pay for.
You can try Reverse cell phone look up , they're quick and offer complete information - not just a surname with a page of possible first names, like some reverse cell phone look up companies do.
I use their reverse look up service and have found them to be very professional.
All the best,
Cheers.