Basil isn’t a name you hear much nowadays. Not in English at least, though it’s a little more popular in its French form. Perhaps it would be more popular if people knew what it meant.
It comes from the Ancient Greek Basileios (kingly, royal), itself derived from the word basileus (king). Not so shabby now, eh? Other related words include the plant, basil, so called because it may have been used in making royal perfumes. Basilica has similar origins, coming from the Latin word basilica (building of a court of justice, or church modelled on such a building), which came from the Greek basilike (royal portal). In Ancient Rome, basilica was used to refer to the seven principal churches founded by Constantine. Fantasy and role-playing-game enthusiasts might also be familiar with the basilisk: a mythical lizard whose name means little king, apparently because it had a crest that looked like a crown. Apparently, because they’ve never existed.
If you’re still not sold on Basil, perhaps one of these other common regal English names (i.e. used commonly by native speakers) will be more to your liking. All of them have the meaning of a royal title such as king, queen, prince, or princess from various:
King Oswald and Queen Tallulah, sounds quite regal, no?