Brian Mc
I have always taken this as the use of the title "Christian" ... as the early believers were taught that Christ (the Anointed) resided in them "as soon as they believed" ... & showed that by following Jesus' lead of full immersion Baptism in the Jordan River ... leaving the old Jesus (the carpenter) behind & coming up as Jesus Christ (the anointed) (see John 14:23, etc. plus Gal 2:20) They would have made this known among others (non-believers) & as they passed along, people likely said, "Here come those Christ-ins" ... this was adapted to be "Here come those Christians.
So a "true" believer is one who ... no longer I who live, but Christ Jesus who lives in me! PLUS John 14:23 states that Father, Lord Jesus will make their abode (dwelling place) in a believer who abides by all the "rules & teaching" ...
someone who has become a "new creation" 2 Cor 5:17 ... grafted into the True Vine by Father so that all that Jesus has & is flows into the branch (part of the Body of Christ) moment, by moment!