Are you looking for a website that gives you the name of a phone number owner for free? If yes, let me assure you upfront that you are on a very difficult quest. The number of website that do offer free reverse phone lookup is almost null.
Being said that, if you are looking for the information on landline numbers, you can always look them up on some white pages. They will have names for most of the landline owners who have not opted themselves out of such directory listing. For cell phone numbers, however, there is no way you can get a name for free. The most you can get for any cell phone number is the city and state where the cell phone number is registered. But for the name, you definitely have to pay.
There are some good websites that let you run some lookups by registering for their trial membership. You can probably use their trial service to lookup the numbers, if you want to look up only a couple of numbers. If you have several numbers, and do have to perform reverse phone lookups in the future too, it will be a good idea to buy a membership of a cheap and reliable service.
Most websites that claim to host a huge database for phone numbers have out dated data on those numbers. Their database has not been updated for years, and they do not even have any reliable source of data. There have been cases where people simply fill in random names for phone numbers, so they at least have some information to display to their customers, even though they are not real.
A good suggestion to follow is to find a reliable website that actually contains information on phone numbers, and get their trial membership. Once you have tested their service with a trial membership, you can always go ahead and purchase a full membership; or just in case, if you are not satisfied with their service, you can always cancel the membership.