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Source: https://writers.stackexchange.com/a/33357
License name: CC BY-SA 3.0
License URL: https://creativecommons.org/licenses/by-sa/3.0/

Two good answers already, so I'll concentrate on the word "relevant".

If the narrator is relevant (someone who personally participated in the events of the story) but his name is not, there might be an advantage in preserving an air of mystery or avoiding distraction from the main characters, but there might also be a disadvantage if the reader was to think "who is telling us this?". If other characters interact with the narrator and he or she is not named, this is likely to become relevant whether the writer wants that or not - there would have to be a reason why they are never named.

If the narrator is less relevant (someone relating a story someone else told them) it's a case of what the writer thinks works best.

For a narrator who is irrelevant (most writing with an omniscient narrator, but not if omniscience is a character trait - for example a deity or pervading artificial intelligence - in which case the narrator becomes relevant) it would usually be best if they are not named.

I'll add a standard proviso about writing - there are rules, but if the writing is done well the rules themselves become less.. um.. relevant.

Original score: 3