In journalistic tradition, the person's full name appears the first time they are mentioned, and thereafter in the article, only their surname is used.
For example, "Senator Joe Biggins, (party, state), introduced a bill to... blah, blah, blah, blah... Due to public outcry, however, Biggins was forced to reverse his position. (Don't we wish! LOL)
However, in story telling, the first name is the more usual convention. That said, you don't want to overdo it, and use their name every single time they are mentioned.
The context of the story should be able to make it clear about whom the author is writing by the use of the personal pronouns "he" or "she." Use of the name again is appropriate if there has been a passage of time (i.e., several pages of action) without mention of the person. But if you are in the same time frame, don't keep saying "Joe" over and over again. It becomes a distraction.
You don't want to see, "Joe Biggins drove down the road impatiently, as he was late for an appointment. Joe was getting angrier and angrier that he seemed to hit every red light. Joe was so mad that he ended up spilling his coffee in his lap. Joe had to take even more time, to go home and change his clothes. This made Joe's mood ever more foul."
Instead, you would substitute "he" or "his" for all the subsequent uses of "Joe" in those sentences.
So, in the end, it depends upon what you are writing: a newspaper or magazine article dealing in facts, or a fictional piece of whatever type.