My answer to: (To vote and comment on Quora, visit the link here.)
1. The names can be transliterated the most accurately to the Roman script as “Rāma”, “Rāvaṇa”, “Lakṣmaṇa” and “Arjuna”. The following three are inaccurate forms:
2. Taking the schwa deletion practice into account while transliterating, the most accurate transliteration is “Rām”, “Rāvaṇ”, “Lakṣmaṇ” and “Arjun”.
3. Taking the schwa deletion practice into account, but ignoring the exact vowels (ā for आ), and consonants (ṇa for ण, and ṣa for ष) (assuming them to be understood by the reader), the spellings become “Ram”, “Ravan”, “Lakshman”, “Arjun”.
4. In an attempt to transliterate according to the actual Sanskrit pronunciation (i.e. without the schwa deletion), but taking liberty of ignoring the accurate vowels and consonants (assuming them to be understood by the reader), the spellings become “Rama”, “Ravana”, “Lakshman” and “Arjun”.
I hope that helps into figuring out where the spellings come from, and what is correct and what is not.