Should we call ourselves Christians? You have to admit that the term Christian has been cheapened. The vast majority of Americans and Westerners consider themselves to be Christians. To be a Christian in today's society is not necessarily anything extraordinary or controversial.
What does the Bible say? The term Christian is only used 3 times in the New Testament. (It was rare during the New Testament period, and most probably used in a derogatory sense.)
Alternatives? The term believer is a term used often in the Church today. But the term only appears 13 times in Acts, and then only 13 other times in the rest of the New Testament. The best alternative to Christian would be disciple. Unlike Christian or believer, the term disciple is challenging. Sure, everyone is a Christian, and everyone believes in Jesus, but how many people are willing to call themselves disciples? The word disciple carries with it the sense of being a follower or a student of our Teacher and Master, Y'shua (Jesus). In addition, the term disciple is used more than 260 times in the New Testament!