So if a king born as an Eastern Chalukya prince became the King of Cholas and was a person of character enough to name himself Chola not Chalukya which practice was followed by his succeeding kings which is borne out by not a single inscription or reference of Kings after Kulothunga I among Cholas named himself a Chalukya or Chola or even Chola Chalukya  By the same token Veera Ballala II was son in law or father in law of Kulothunga III then why were the Hoysala kings after him not called as Chola Hoysalas or Hoysala Cholas or even as admitted by you in the Chalukya page Vikramaditya VI was son in law of Veera Rajendra then why were his successors not called Chola Chalukyas or Chalukya Cholas  Going by the same analogy not a single Chalukya king after Vikramaditya VI deserved to be called only Chalukya or Western Chalukya but only Chalukya Cholas  May I again remind you that not a single friend of adversary of any king from Kulothunga Chola I has called Kulothunga I and his successors as a Chalukya Chola but only Chola or by their epithets like Tribhuvana Chakravartin etc etc