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 Dimitri mean?
Dimitri honours Demeter, the Greek goddess of the harvest and earth.