"Hello" is fine. It is polite in all situations. I'm a native U.S. speaker. If there is any special phrase for a greeting during "the wee hours of the night," I don't know what it is. If it's New Year's Eve, of course, you'd say "Happy New Year!" If you work a late shift and have a job answering the phone, I'm sure your employer will have their own guideline. Actually, even among native speakers, phrases like "good morning," and "good afternoon," and "good evening" get awkward when it is close to a borderline time. It turns into a brief uncomfortable moment when someone says something like "Good morning... uh... I mean good afternoon," and it forces both people to check their watches, and actually calls attention to the speaker's mistake. "Good morning" when it is the middle of the night and pitch-black is surprising to the listener, and may even be uncomfortable because you are reminding them that they have been up later than they think. I wouldn't say "good morning" unless it is 4 a.m. or later, and there's some trace of light in the sky, or it is the beginning of a work shift that extends well into daylight.