The name is derived from Sanskrit “Rama” (the deity-hero of that name) + “anuja” “later-born”, i.e., the younger brother of Rama, namely the hero Laksmana.
Which is correct. That’s because, as you noted, the “a” in the syllables “Ra” and “ma” is long, so the syllable is heavy in both cases. The syllables “nu” and “jan” are light, since they have short vowels and no double consonants. So the heavy syllables get the stress.
The common western pronunciation “Rama-NU-jan” probably evolved in erroneous imitation of more familiar four-syllable non-Indic names such as “Alexander”, “Amadeus”, “Obadiah”, etc.