Of course Jesus never called himself a Christian! The term "Christian" is generally understood to mean a follower of Christ. Jesus wasn't a follower of Christ, he was the Christ.
When it comes to modern usage in the greater culture, things get complicated. The term "Christian" is not trademarked. Linguistically, no group has more right than another to use or not use the term at their will. Frankly, the term means something different to everyone that uses it. Whether they are "truly" Christian has almost nothing to do with whether they do or don't label themselves as Christian or whether an outside would label them that way.
For the purposes of this Stack Exchange site, our local scope has been defined as including all established groups that self identify with the label "Christian" and excluding everybody who does not. This is not the actual definition of "Christian" used by any of us for our own purposes. Each tradition is going to have a different view on what counts as a a valid expression of Christianity and what does not.
I personally know people who refuse to use the term Christian for themselves even through I believe their faith to be quite orthodox, as well as others who insist on using the term even though they are outright heretics. Whether I would label them as Christian according to my doctrinal position is almost inconsequential in whether they would consider themselves Christian.
When push comes to shove, the term isn't very useful except as a broad cultural classification. If you want to identify the actual beliefs of a group, you must use a more specific term (which is why most questions on this site must be scoped to some tradition smaller than just "Christian").
TL;DR: Claiming to be Christian doesn't make you anything except somebody who claims to be Christian. By the standards of any Christian, actually being saved and a follower of Christ is not closely related to the usage of that term.