I've heard the 'n' in "Me llaman Carlos" voiced as [ŋ] (the "ng" sound in English).
Is it ever correct to voice it as "Me ʝaman kaɾlos"?
Under what circumstances is 'n' voiced as [ŋ] versus [n]?
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This is a normal feature of Spanish (and indeed many other languages) called assimilation. More specifically, in this instance, it's called anticipatory coarticulation.
When the normally alveolar voiced nasal /n/ immediately precedes a velar (for Spanish you have /k/, /g/, and /x/), the articulatory position of the /n/ is pushed back in preparation for the velar sound, thus being realized as the allophone [ŋ] instead of the "default" [n]. This makes the sound of the two letters closer, and easier to say.
It's perfectly correct and indeed expected, such that not doing it will sound a bit off and overenunciated. But don't think about it, your mouth/tongue will generally take care of it automatically when speaking.
(Also there are some dialects that word/phrase finally do this naturally to all /n/, if I remember correctly, but I can't recall which at the moment)