I would suggest using the names when appropriate and, if the character is POV, introduce him to the readers using the name he would prefer the readers to call him. To give a modern example, if I was writing about a character with the name "James Tiberius Kirk", he would use different names with different people. James Tiberius Kirk is his legal name and would be used in a formal or legal context (Say an academy admissions form or a disciplianry hearing), where as using pet names of Jimmy might be family and close friends, Jim might be more friends or very close working collegues, J.T. might be among his primary (elementary, middle, and high school) friends, to whom he felt James/Jimmy/Jim was too common or silly and the first and second name initials are way to cool (especially if the name is an unfortunate name pun after a pop culture icon... Looking at you, Degrassi). And to those to whom his job makes him a superior to, he might use his last name only with an appropriate title (Mr. Kirk, if he was teaching a classroom of students... Captain Kirk if he was a commanding officer on an Enterprising vessle of exploration).
The reader however, should be introduced to the character in a way the character calls himself (James Kirk) unless their is a significance to a dual identity nature that we should establish. This exception usually comes up in cases where there is an alter ego (Batman/Bruce Wayne) or more (Clark Kent/Kal-El/Superman). The two selected individuals are highlighted because among superhero fans, they often stand in contrast to one another in how they are precieved. To the later, the character is Clark Kent, while his birthname is Kal-El, and his created public persona is Superman. To the former, many fans will argue that "Batman" is the character, while Bruce Wayne is both a birth name and a created public persona (often writers will go out of the way to show that Bruce Wayne, when talking to himself, calls himself "Batman" rather than Bruce. Contrasted, Superman will call himself "Clark" when talking to himself.).