There are many ways to answer this question. Let me just be clear, LIFE IS THE MOST PRECIOUS GIFT GOD HAS GIVEN US. Now that I got that out of the way. Lets looks at a couple scenarios.
A person comes to someones house and intends to kill a whole family. The husband is the only one they caught but the rest of his family is in the basement not to be found. Lets say a wife and 5 kids. If they ask him about his faith and he says Catholic and they ask where is his family, of course he shouldn’t tell them. This is just my opinion. The man will save his family and become a martyr for dying for his faith.
If a shooter is on the loose and lines up people and asks about their faith and if they are Catholic or believe in Christ. Yes they should say they are Christian. The crown of Martyrdom is something nothing in this world can provide, ETERNAL HAPPINESS. It is important to understand that Jesus will be with us in those moments no doubt and God will give us the grace to be courageous. God gives us grace in all situations because he is constantly leading us.
What im trying to say is, never deny your faith in any circumstance. I mean any. What happens when you die and you just deny your faith and you meet Christ face to face as it is promised to us, and he says, “You denied me, I do not know you.” Of course I am not sure what he would say but lets look at scripture and the parable of the Narrow Door:
The Narrow Door; Salvation and Rejection.*
22 He passed through towns and villages, teaching as he went and making his way to Jerusalem. 23 **Someone asked him, “Lord, will only a few people be saved?” He answered them, 24 “Strive to enter through the narrow door, for many, I tell you, will attempt to enter but will not be strong enough. 25 After the master of the house has arisen and locked the door, then will you stand outside knocking and saying, ‘Lord, open the door for us.’ He will say to you in reply, ‘I do not know where you are from.’26 And you will say, ‘We ate and drank in your company and you taught in our streets.’ 27 Then he will say to you, ‘I do not know where [you] are from. Depart from me, all you evildoers!’ **28 And there will be wailing and grinding of teeth when you see Abraham, Isaac, and Jacob and all the prophets in the kingdom of God and you yourselves cast out. 29 And people will come from the east and the west and from the north and the south and will recline at table in the kingdom of God. 30 For behold, some are last who will be first, and some are first who will be last.”