Then why is Catlyn Stark called Stark half the times and Tully another. Not disagreeing with you but just pointing out the inconsistency.
she wasn't a queen, same as her sister Lysa Arryn had the lords name but Margerie stayed Tyrell. I don't remeber anyone actually calling Catlyn as Tully, she's definately referenced as a Tully alot but don't recall any Lady Tully or Catlyn Tully