Strictly speaking, it's "Серафима", with "м". Obviously the concept of translation is pretty vague when it comes to names, after all, Peter is not Пётр. However everyone who is named Seraphina in Italian, Spanish or Latin usually (but not always! - see below) is called "Серафима" in Russian.
Why in some languages this name is with "n" and in some with "m" is outside of the scope of Russian SE, but here you can find more on the origin of the male version of the name and it will give you a hint how both versions originated.
As of why specifically in Russian it's "Серафима", not "Зерафина" or "Зерафима" - well, because it was borrowed through Greek where it was in this particular form.
But again, translating names and transliterating them are different things. I can imagine that in modern media one can try to transliterate the name rather than use Russian counterpart, even though very similar. In that case it would be Серафина, your friend is right.
For instance, Séraphine Louis, a French painter, is always referred as Серафина Луи in Russian sources, while, for instance, catholic saint Seraphina di Dio is Серафима in Russian.
UPD: Now that it's clear that the author is a native German speaker I want to add a couple of things about transliteration of initial German S followed by a vowel in general. @svavil added a very useful link about German transcription in general, it is still not fully complete.
It is claimed in that article that s followed by a vowel is passes as "з". For personal names it's actually more complicated than that. Rule of thumb would be that if name considered sort of pure German and has no obvious counterparts in non-Germanic languages, it would be with "з", so we got Зигфрид. If, on the other hand, this name is not associated purely with, so to speak, Germanic world, we still get "c". That's why, for instance, Simon which sounds way more closer to a Russian speaker to "Зимон" in its German shape, is still most likely would be passed as "Cимон" in Russian. The same, for instance, with Sebastian (Себастьян).