This is an interesting question, but it has more to do with English and its phonology than it does Japanese. I think those Japanese users on Yahoo who state they hear 「アナ」 in the English version of the movie pretty much hit it on the mark.
tl;dr: You don't nasalize the first vowel /æ/ when pronouncing that name in English, unlike some other languages, thus creating a difference between translations of that name from various languages, represented by that ン.
English is not a nasal language, as is often said about the language when compared to other similarly widely spoken languages like French or Portuguese. Yes, it's true English doesn't have fully nasalized vowels as French, Portuguese, and some other languages do. But there's a twist: partial nasalization of vowels does occur in English. Let me give you a few examples to illustrate this point which I think any fluent speaker of English will get.
When you say this word, you simply go from the consonant /m/ to the vowel /i/ and there is nothing to follow /i/ which brings up the rear. There is no nasality involved after /m/. When executing the vowel all air goes through the mouth.
When you say this word, you go from /m/ to /i/, and then conclude with the nasal /n/. The magic happens before you go into nasal mode. Most English speakers, when they get ready for the nasal consonant, partially nasalize the preceding vowel, which in this case is /i/. The nasal flap in the back of your mouth, situated around the soft palate, diverts the air and channels part of it to the nasal passage. Try and pronounce it a few times and you will get the idea.
When you pronounce this word, the partial nasalization process that happens with "mean" doesn't happen here, because of this other phenomenon in English: partial nasalization doesn't occur in the same word if the only sound between them is a nasal consonant. So with "meaning" you don't nasalize the /i/. In fact it is an often heard mistake from English learners to nasalize vowels in words like this.
Again nasalization is possible here because between /eɪ/ and /ɪ/ there are two consonants now /nt/ and there is a break after the nasal /n/. And thus partial nasalization can occur with the diphthong /eɪ/.
* Note: I borrowed Macmillan English Dictionary's phonetic symbols which might deviate ever so slightly from the standard IPA but that's really not important here.
Back to Anna. The pronunciation of the name Anna /ˈænə/ follows the same rules (I say rules but these things are descriptive, namely they describe how natural speech is). That tells us you don't nasalize the first vowel and you shouldn't add an extra ン when you transcribe it in Japanese, which is exactly what the translators did here. It is a clear-cut /æ/ + /nə/. And that's why to a lot of Japanese ears it sounds like アナ, as it should.
In comparison, the name Anna (Анна) is pronounced differently in Russian with distinct nasalization. Listen to this. That's why the Japanese title of Leo Tolstoy's «Анна Каренина» is アンナ・カレーニナ.