People seem to be thrown off by the misdefinition of what faith actually is, namely they take an "outward" definition as being "saying they have faith" is equivalent to having faith… because it wouldn't be polite not to accept those claims. The reality is that someone who has actually placed their faith in Christ has done something much more substantial than outwardly claim to have something, and this is of course reflected in their every action, as they have, in fact, (not simply claimed to), repented of their former belief– which is that something else might save them, which everyone has at some point held when they were unbelievers– and has in fact (not merely claimed) turned away from the power of satan and to the power of God. We see from what Paul said in Acts 26:18-20 that there is the repentance itself and there are works fit for repentance, so that both occur together but one is the cause of the other, with faith coming first and good works being made possible afterward.
However, according to Paul in Romans, 1 Corinthians and Ephesians, we should be careful not to take credit for the work of God in our lives, as "boasting is excluded" and we are saved by grace through faith, "lest any man should boast." So we should not be taking credit for what is truly not our work but only God working through us.
It is also quite strongly spelled out for us by Paul in Philippians 1:6 that once God has begun a work in someone, we are confident that He will perform it until the day of Christ. This keeps well in line with eternal security of the believer as spelled out elsewhere (John 5:24, Acts 13:48, Romans 8:29-30, 2Cor. 1:21-22, Ephesians 1:11-14, 1 Peter 1:3-5, 1 John 5:13).