The lives of the converts were so different from their unbelieving neighbors, that they were called Christians. It is supposed that the name was given them in mockery or contempt by the heathen people of Antioch. But the name stuck, and is now used universally to describe those who follow Christ. It may not be the very best of names.
Perhaps disciples is better--disciples means learners, followers. We should all be disciples of Christ and should ever be learning of Him, growing in grace and likeness of Him as we follow Him.
Perhaps believers is a better name. It carries in itself the thought that we are saved by believing on Christ. It is faith which works the victories in this world.
Perhaps followers would be better. To follow Christ is to receive Him as Master and to cling to Him in obedience and devotion wherever we may go.
I too often hear people say, "Oh, they're a Christian...they believe in Jesus." Unfortunately, whoever believes that is deceived. Many people believe that Jesus was a real person, but that doesn't make them a Christian. A true biblical Christian does a lot more than believe. A true biblical Christian knows, without a doubt in their mind, that God sent His only Son to suffer and die on the cross to save us from our sins. And that knowledge drives that person to repentance (completely turning from their sin). So the next time someone tells you they are a Christian, don't be afraid to ask them to explain to you what that means. If they can't give you a biblical answer, share the truth with them and pray that God would speak to their heart and that they would come to know Him before it's eternally to late for them.