What does Advik mean?
A modern Sanskrit-derived name generally glossed as 'unique, one of a kind', linked to the idea of advitiya ('without a second, incomparable'). The further association with advaita ('non-duality') is thematic rather than a direct etymology.
What does Neel mean?
From the Sanskrit नील (nīla), 'dark blue, indigo, sapphire'. A genuine classical colour word, also the root of 'neelam' (sapphire). Note: the similar-looking English/Irish name Neil (from Gaelic Niall) is a separate, unrelated name.