This discussion is based on M-M's Vocabulary of the New Testament.
BASILEUS was a title adopted by Alexander the Great and it was used by his successors "in the Syrian and Egyptian monarchies." It was a title known to Jews of the Diaspora and later came to be applied to the Roman Emperor.
Concerning the title BASILEUS BASILEWN (Rev 17:14; 19:16), Deissmann presented evidence that this phrase was "in very early Eastern history a decoration of actual great monarchs and also a divine title." Furthermore, "Dittenberger (p. 648) contests Strack's attempt to claim BASILEUS as well as BASILISSA as a term applicable to non-regnant members of a royal family: he notes that there is all the difference between BASILEUS and its feminine. Wilcken Archiv iii. p. 319 supports him, and notes inscriptions where BASILEUS is promptly dropped when a mere H. R. H. is named after the king and his consort. He also commends Dittenberger's remark that Augustus and Augusta had the same difference after Domitian's time."