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 Agni mean?
Sanskrit for 'fire' and the name of the Vedic Hindu fire god, who carries sacrificial offerings to the gods. The word is cognate with Latin 'ignis'.