For example, a man's name is Jeff Smith. My question is:
When should I call him "Jeff"?
When should I call him "Smith"?
When should I call him "Jeff Smith"?
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In general US usage, you would use "Jeff" if you are friends, contemporaries, or Jeff has asked you to use his first name. First names are often used in casual settings.
You would use "Mr. Smith" (or "Dr. Smith" or other appropriate title) if you are colleagues, younger than Mr. Smith, or in a formal or business setting.
You would use "Smith" in a very casual setting, particularly when playing sports.
You would use "Jeff Smith" when making an introduction, or if you needed to distinguish him from other Jeffs or Smiths, or sometimes when greeting him.
Usually you refer to someone by their last name when it is more formal so, if they were your boss, or some other form of authority or perhaps, someone you just met.
You use someone's first name more casually, if you know them personally better.