What does Ansh mean?
From Sanskrit amsha (अंश), 'portion, share, part'. Often used affectionately to mean 'a part of oneself' or a share of the divine.
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.