I am not a Christian but I find pleasure in reading religions including Christianity. Recently, I was surprised to discover that you can still be a Christain even though you believe in Nontrinitarianism and reject the existence of the Holy Trinity. interestingly, the New Testament does not mention the Trinity (that is according to a paper published by Stanford University.
The word "Christian" is a label, so we find many people with quite varied beliefs calling themselves Christians, some outside the pale of what is normally considered Christian (e.g., acceptance of Nicene Creed as in this site's Statement of Faith). Most Christians I know would not consider non-trinitarians to be Christians.
No, the NT does not mention the term, trinity, but it does mention persons of the trinity as in Matthew 28:
19 "Therefore go and make disciples of all nations, baptizing them in the name
of the Father and of the Son and of the Holy Spirit,"