Well, I believe that I pretty much DID define a "Christian" as someone who believes in Jesus, didn't I?
(thinking) yes, I do believe I did. I DID also add the 'and claims to be a Christian" to that, because, well...all sorts of people believe in Jesus who don't claim to be Christian. Muslims also believe in Jesus. Not quite the way Christians do, of course, but they do believe in Him. They don't even have problems with the virgin birth. They DO, if I have their beliefs right (and I may not) have problems with the crucifixion/resurrection, but they believe He existed and might even have been the Jewish Messiah.
Again, I COULD have that wrong. Any Muslim reading this who wants to correct me, feel free. I would be grateful. They don't put His teachings at the center of their belief system, though, and they do NOT claim to be Christian.
As to your reference to scripture...I surely did not see the word 'Christian' in there anywhere.
The NT has several letters in it written by apostles to erring churches who were beginning to stray from the 'straight and narrow,' so to speak. In other words, their beliefs weren't, quite, correct. Yet they were....as the disciples of Christ were 'first called Christian' in Antioch (Acts 11:26)...called 'Christian" themselves. So...believing in Jesus is important. Being RIGHT about those beliefs? Not so much. Not to be "Christian."
All that does is mention that other people decided to call this particular group "Christians." Who knows why? Did they call THEMSELVES that? Or, as happened with the Mormons, was the word first applied to them in an extremely mocking manner meant to denigrate and demean, but which was adopted by those followers of Christ as a sort of 'badge of honor?'
That's what happened, with the Baptists, Lutherans, Quakers, the Shakers and the Mormons, come to think of it. It seems a fairly common thing to do, for the despised minority to grab a mocking and supposedly demeaning appellation and turn it around and flaunt it. Certainly the only other two times it was used in the NT, it WAS used in a manner that more than hinted at its demeaning origin.
What the NT does NOT do is associate "Christian" with salvation...or even to believing the 'correct things' about Jesus.
"Christian" means, as you have just indicated, that someone puts the teachings of Jesus ('believes in Jesus") at the center of his belief system, and claims the classification.
Anything else? "True Christian" territory.
Of course the NT associates Christians with salvation. The verse I quoted as a definition(Jn 3:16) says beleif in Jesus results in eternal live---that is salvation. There are many, many many more.