Much of Utena's Japanese cultural context is really hard to access as an outsider. I literally just poked around with a basic search and Wikipedia trawl and found out that Arisugawa & Saionji are both names derived from different ranks of Japanese aristocracy.
Not only that, but during the Meiji restoration and US occupation, nobility were reorganized under the British model, making "Prince" the highest title, just like in Ohtori.
Utena's basic structure includes the premise of a Japanese world order restructured along the lines of British nobility, and this is shown in aesthetics and the class character of the student council and Ohtori Academy as a whole.
The academic institution itself, with its army and navy based uniforms, has historically been the site of elite cultural production in Japan as well. The way these characters navigate personal, financial, and institutional privilege has much more specific context than I realized as an American viewer. Utena as a text reflects not just patriarchy and race but also cultural imperialism.
