This has been an unexpected joy for me, to experience such complete concordance between the spelling and the pronunciation. Plus additional realisation of how useless English spelling is.
Where does the second “e” come in in Peter? To me it seems like it should be Petr, unless r by itself assumes the er sound
I suppose you are referring to the transliteration of पीटर in English. As Peter is already a name with a widely-accepted spelling, there is no different way to translate the Hindi word into English with a different spelling. As far as the word पीटर is concerned, it is spelt in Hindi the way an Indian ear perceives the pronunciation of the word "Peter", where the second vowel sound is a part of the second syllable: Pee-Tuhr. So, the second 'e' sound materialises with 'ट' (t) in पीटर. :)