What does Basil mean?
From Greek 'basileios', meaning 'kingly, royal', derived from 'basileus' ('king'). Carried by Saint Basil the Great. The sense is the adjective 'royal/kingly' rather than the noun 'king'. (The herb shares the same root.)
What does Isidore mean?
From Greek Isidoros, combining the goddess name Isis + doron 'gift' — 'gift of Isis'. The 'gift' element (doron) is the same one found in Theodore and Dorothea; here the giver is the Egyptian goddess rather than God.