Lore question regarding Oceiros

So this is something that has bothered me for quite a while - who is the official ruler of the Kingdom of Lothric? It's clear to me that Lothric is the de facto head of state, but why is he only referred to as "prince"? Is Oceiros still the official ruler of the kingdom, and therefore Lothric cannot legally be a king? For a long time I thought he was banished into the Consumed Garden after going mad, but recently I read a theory that suggested he went there himself in order to hide from everything after going mad. If that is the case, are the Twin Princes aware of the whereabouts of their father, are they not allowed to enter the garden, or is he assumed to be dead?