This page has information about the Battle Chateau on Rivière Walk, including a list of noble titles that can be earned.
Every few hours, new nobles arrive in the Battle Chateau that you can battle. A new noble may show up while you are in the Battle Chateau. This will be announced after you go through any door in the chateau.
When you achieve the level of Marquis/Marchioness, you might find gym leaders in the chateau. When you become a Duke/Duchess, you might find member of the Elite Four in the chateau.
If you talk to the maid near the entrance of the Battle Chateau, you can ask to send a writ. It costs 50000 Pokédollars to send a writ. The type of writ you send will have a specific effect on the nobility that come to the Chateau, listed below.
By default, your first noble title is Baron/Baronness. As you defeat more nobles in the Battle Chateau, your title changes.