Sidenote: That's a really weird way of writing his first name. While the Russian does have a letter that visually resembles ë (unicode: ё), it is not a variation of the letter e as this transcription suggests, but invariably pronounced something like 'yo'. The name is pronounced "Pyotr", and of course corresponds to Peter, by which name Kropotkin was also known. I've no idea where this spelling comes from, but it's like writing Bladimir or Cergei instead Vladimir Sergey. Weird.
Of all the choices[1], I’ve always been partial to the ISO 9 / GOST approach with Czech/Slovak-style diacritics (either version), even though those same diacritics make it impractical in most ASCII contexts. Just now I went to check the table and learned it actually prescribes ë for ‹ё›. Huh.
I actually like this spelling. The sounds that have exact equivalents use the Latin alphabet and those that do not are replaced by the character's native system. Cause his name is not Pyotr or Peter or Pierre or whatever else. It is Pëtr indeed.
I'd say Pötr would be a (technically) correct transcription, although it looks super weird.
On pronunciation: “Pyotr” is most close, if you use the “y” just to note that the “p” is soft and not as a separate sound – i. e. “Pjotr” would be incorrect.
PS: Read Kropotkin, he's good.