While cellphone companies do not publish directories listing their customers' names and phone numbers, it is possible to find out who a mobile phone number belongs to by doing a little sleuthing online. There are people search sites that often provide this information, but they usually charge a small fee.
If you receive a mobile phone call and do not recognize the number, you have a few choices to track down who called you. First, try googling the number to see what information you find. Include the area code when you enter it into the Google search bar. If the call came from a business or anyone who wants to be reachable by the public, you are likely to find the number and its source in your search results. Since the number is through a mobile carrier, you cannot use a reverse phone number lookup service to track it as cellphone numbers are expressly excluded from these services. Instead, try using a people search service such as Intellius or Spokeo to see if you can find who owns the number. A final choice for finding out who a mobile number belongs to is simply to call the number and determine who answers.