'Trinity' is an English word for the concept of three. The term Holy Trinity is commonly used and we all know what it means. The concept can be seen in the Bible but it's not written in those terms. There's nothing to using the word trinity to describe 3 of something as long as it isn't used to relate them to the Lord.
God won't ever give up on anyone unless they turn their back on him. There's no sin that he won't forgive other than the one against the Spirit. Keep this in mind:
Rom 8:29 For those whom he foreknew he also predestined to be conformed to the image of his Son, in order that he might be the firstborn among many brothers.
30 And those whom he predestined he also called, and those whom he called he also justified, and those whom he justified he also glorified.
I've seen this passage used many times but they always skip the 1st step - 'foreknew'. That means that God knows from the creation who will answer and those are the ones who get the call. We all have free choice but God knows what that choice will be. He won't call anyone who he knows won't answer. If he foreknows that a person will answer, it won't affect their salvation if they use his name in vain. He will forgive them. He doesn't want us to sin, of course, but he will forgive it.
