What does Egan mean?
Anglicized form of the surname Mac Aodhagain, 'son of Aodhagan', where Aodhagan is a double diminutive of Aodh ('fire'). The fire sense is inherited from that root rather than the name itself.
What does Conall mean?
Popularly glossed as 'strong wolf', from Old Irish 'con' ('hound/wolf') plus a second element. This is DISPUTED: the rigorous etymology derives it from Proto-Celtic *kuno- ('hound') + *walos ('prince, chief'), giving 'strong hound' or 'mighty chief' rather than literally 'wolf'. Flagged as uncertain.