#but sadly there's more evidence for RaMpo

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Is it Ranpo or Rampo? PSA since the spelling is different between subs:

The real life author Edogawa Ranpo/Rampo was a very cool person. There are lots of fun stories about him, but the thing to know is that he liked Edgar Allan Poe and could speak English. (He liked Poe's mystery stories specifically, Poe having created the proto-Sherlock in his stories about character C. Auguste Dupin).

Why RaNpo: The original author based his pen name on Edgar Allan Poe like so:

Edgar Allan Poe -> Edga aran po -> Edgaa ranpo -> Edogawa Ranpo -> えどがわ•らんぽ ->　江戸川•乱歩

Because of the Japanese phonetic system, the O in "Ed(o)" is considered "soft" and can be skipped over when talking fast, and the W sound is so soft it's often omitted from translation altogether. The Rs are a little more complicated but for the purposes of this explanation I'll just say that soft Rs at the ends of English words are often omitted in their Japanese counterparts (i.e. "computer" is pronounced "computa"), and Japanese doesn't have an L sound exactly, so the R in Ranpo is a stand-in.

So. This makes it seem like a no-brainer to spell it Ranpo. I'll give another point in Ranpo's favor: Japanese does not have a stand-alone character for M. Each Japanese character has at least two letter sounds in it and one is always a vowel (thus "do" instead of just "d" in Edogawa). Vowel-only sounds are an exception to this rule. They have characters that represent solo A, E, I, O, U sounds - and one for N. ん is just the letter N. They do have the M sound of course, and Ranpo is written "Ra-n-po" so this must mean it's Ranpo, right?

Why RaMpo:

Now it gets complicated. As previously mentioned, Edogawa Rampo could read and speak English. He couldn't write it, however, and so in the 1950s he collaborated with a translator to translate his works into English. His chosen romanization of his pen name? Edogawa Rampo.

Now we KNOW he knew better. He can read English and he's a huge Poe fan, he knows this isn't how Allan is spelled. I haven't been able to find anything on his reasoning, but nobody in the US even realizes this is a play on Poe's name upon hearing it, so I doubt copyright had anything to do with the spelling (and they got way fewer claims for that in the 1950s anyway). I will say that I've seen quite a few Japanese people choose handles related to things they like in German/English and then choose to spell it differently in the romanization, so it might just be for fun. But whatever the reason, the fact remains that Edogawa Rampo himself spelled it Rampo.

On the use of ん, a translator friend of mine once explained the phonetics of the ん character to me. If you're an avid weeb you might have seen "senpai" spelled "sempai" on occasion. You know how the letter A has long and short pronunciations (denoted by "ā" and "ă" respectively)? Similarly, ん has 4 different pronunciations depending on the sounds around it. The most common one is indeed the N sound English-speakers are familiar with, but if ん comes before a sound where your lips press together (such as M, B, or P) it's pronounced like an M. Rampo has one of these sounds following the ん. Traditional Hepburn (the oldest popular style guide first published in 1867) recommended using an M in these cases. Revised Hepburn, which was published in 1908 and instead suggests using N in all situations, has since become more popular and many insist it's "correct," but in reality both are still quite common - for example, few people have switched to calling tempura "tenpura." (As Edogawa Rampo's first translated stories came to the US in 1956, this isn't a definitive reason for him to have chosen either spelling, but it at least explains the inconsistency in translations.)

Since these style guides are prevalent in Japan, it's possible that Edogawa was just following one of those in his chosen translation. Or he might have been being artistic. Someone out there may know but I sure don't.

As a final note for Rampo, all of the official Japanese merch uses the M spelling. I take any and all official merch spellings with a grain of salt, but in this case it's very consistent. Funimation's written romanization has been Rampo (check season 2), but Yen Press has used Ranpo.

So what's the answer?

Technically both are "right," it just depends on your style guide (and, personally, I like Ranpo better), so the answer is... use whichever you like! Such is the way of romanization in anime fandoms.