N-no, that's not it — it's just that I never imagined there'd be someone who'd need me for who I really am.
Literal
N-no isn't-that, ..., bare [gen-の] self, real [gen-の] I [obj-を] consider-necessary-[-てくれる] person [subj-が] exist [such-a-なんて], think-thing [also-も] didn't-exist [polite-ませんでしたから].
そうじゃなくて is a polite 'that's not it / that's not what I mean' — the て chaining into what follows. 素の自分 '(one's) unadorned / real self,' where 素 (す) means 'unadorned / sober.' ~として必要とする '(to) treat X as necessary / need X' contrasts with the plainer 欲しい or ほしがる. ~てくれる marks the third-party action as a favor to the speaker. ~なんて carries the amazed tone 'the very idea that.' 考えたこともありませんでした is the experience-pattern with こと.