I mentioned in two comments, which were swiftly deleted, (why, I have no idea) that in speech the word Poe might not be understood. For example, if out of the blue someone said:
I love Poe
The listener might ask for confirmation—
Oh! You mean Edgar Allen Poe?
I think the name Edgar would be stressed in speech, someone more expert than I might confirm or disagree and say which word would be stressed.
Regardless, echoing and adding extra info is but a spontaneous and natural reaction, a method to double-check we have understood. In normal speech this takes seconds. In writing the problem is less likely to occur; we see the word Poe and we (should) recognize the author immediately. I made a similar observation about Shaw in a comment (which was deleted), the surname has the same pronunciation as sure. In casual fast speech, a person may hear:
“Was it Shaw who said: ‘All great truths begin as blasphemies’?”
and quickly ask—
“Was what sure?”
“George Bernard Shaw, you nimrod!”
Again, in writing this error is unlikely to occur but in speech? And the OP seemed to refer to people speaking and asking for confirmation, not in writing. Surnames with two or more syllables are less likely to misinterpreted
Mussolini was great
No difficulty there. It's superfluous to add Benito, the same goes for Mozart, Van Gogh, Picasso, Obama, etc.
Finally, I argued that sometimes a first name or last name will mean different things to people according to their background, culture, and interests. If I say "I'm a fan of Jackson" or "I admire Jackson's innovative style" am I referring to the pop singer, Michael Jackson, or the artist Jackson Pollock?
The OP, Ricky also made some interesting observations along with several other users, but these comments were deleted too.
(Do I have an axe to grind? You bet I do)
So, to sum up, the question is subjective but answers can be objective and can offer a possible explanation as to why...
… if you say, "I read this story by Poe," someone is very likely to make absolutely sure by asking, "Edgar Allan Poe?"
Ironically, one of the users who closed the question left this comment—not deleted— saying:
It is an interesting question in its own right, and could stimulate some interesting discussion, but I see no way this can be answered objectively.
The risk of POB questions is that users will post their thoughts, opinions, and their experience in their answers. Things which are discouraged on ELU.
Users have to write answers that are supported by links, Ngrams, citations (which must be properly attributed); any references used in formulating their responses should also be cited, and authoritative sources are preferred, such as the OED.
You can't provide a good objective answer without using any of these props.
Or can you?