Basilika, Ocimum basilicum, is ‘basil’. Latin basilicum comes from greek basilikon ‘regal’ from basileus ‘king’, of unknown origin, possibly from a language of Asia Minor. So called, probably, because it was believed to have been used in making royal perfumes. (Online Etymology Dictionary). Of course basilica, 'church', has the same Greek origin .
Latin Ocimum comes from Greek okimon, an aromatic herb, probably basil (Jen Corneliusson, Växternas namn).
It will soon be time to make pesto now, before they start flowering.