False, if one is in the Body of Christ.
People can be called by what they do.
People who lie, liars; people who steal, theives; people who murder, murderers; etc.
People who sin: Sinners.
People who are saved: Christians.
If we're dead to the law, the law has no hold on us. We're like the woman whose husband has died, she is no longer bound to him. She is released from him, as Paul writes in Romans 7:1-6.
Thus, while it is true that we still sin, we cannot be called sinners, because we are dead to the law. We are identified in Christ! Christ is not a sinner!
Paul writes:
For what I am doing, I do not understand. For what I will to do, that I do not practice; but what I hate, that I do.If, then, I do what I will not to do, I agree with the law that it is good.But now, it is no longer I who do it, but sin that dwells in me.For I know that in me (that is, in my flesh) nothing good dwells; for to will is present with me, but how to perform what is good I do not find.For the good that I will to do, I do not do; but the evil I will not to do, that I practice.Now if I do what I will not to do, it is no longer I who do it, but sin that dwells in me.I find then a law, that evil is present with me, the one who wills to do good.For I delight in the law of God according to the inward man. But I see another law in my members, warring against the law of my mind, and bringing me into captivity to the law of sin which is in my members. O wretched man that I am! Who will deliver me from this body of death?I thank God—through Jesus Christ our Lord! So then, with the mind I myself serve the law of God, but with the flesh the law of sin. - Romans 7:15-25
http://www.biblegateway.com/passage/?search=Romans7:15-25&version=NKJV