What does Nagendra mean?
Sanskrit compound of naga 'serpent' + Indra (as the suffix -endra 'lord, chief'), read as 'lord/king of serpents'. Hedge: the naga element is secure, and this split is the standard reading, but I could not confirm the full compound against a Sanskrit lexicon rather than name-reference sites, so treat the exact gloss as the common interpretation.
What does Nagaraja mean?
From Sanskrit नागराज (nagaraja) 'king of snakes', from naga 'snake/serpent' + raja 'king' (also spelled Nagaraj in Tamil/Kannada/Telugu usage). A well-attested compound; the serpent sense is secure.