Here’s Ramanujan pronounced by an Indian speaker in an Indian documentary.
Here’s how Ramanujan is written in the Devanagari script: रामानुजन्
Which breaks down as:
रा = र + ा = r(a) + aa (long a) = raa
मा = म + ा = m(a) + aa (long a) = maa
नु = न + ु = n(a) + u (short u) = nu
ज = j(a) (short a - if vowel is not written it’s short a) = ja
न् = n(a) (+ virama, which is the little diacritic line at the bottom of the letter which cancels the inherent vowel of the na consonant, making it Ramanujan and not Ramanujana) = n
So “rama-NEW-jin” would be a closer approximation of the pronunciation, although i is a different vowel altogether. The Devanagari small a of the “-nujan” part of the name is the sort of default vowel and is weakly pronounced, perhaps comparable to the sound of the a in “human”.