The Law applied to the Hebrews. Jesus nailed the law to the cross & we as gentiles were never under the law (except Noahide) (Gal. 3:23, Rom 10:4, Eph.2:15)
Christians are under the law of Christ (Gal.6:2). So as other posters have stated, such worshipers of the God of the Bible & following the lead of the apostles are to be called 'Christians' (Acts 11:26).
I suppose their are many denominations who give their church as a whole a specific name to differentiate it from other churches - In the Bible they used only geographical location e.g. church of Ephesus /Brighton /Austin Tx etc - But naming your church or denomination something else is one thing, calling yourselves as Christian's anything else but "Christian" is not Biblical, IMHO.
In recent times Watchtower has leant more towards reclaiming the term Christian, e.g. "Jehovah's Christian Witnesses" (perhaps because they often get challenged that they are not?). But despite their protests they call each other "one of Jehovah's witnesses" first and foremost and always have.
NB. I'm still not clear if Arian's are considered fully Christian? Can someone more knowledgeable clear that up for me, please?