A griffin has taken over a lord's castle with the help of a dozen or so golems, kicking his soldiers, retainers and entire household out while keeping the lord imprisoned in one of the towers. The story picks up after a few weeks after this has happened so I'm wondering in the eyes of the general public, whose castle is it? It's the lord's name and banners above the gates but it's the griffin's nests atop the battlements and its screeches echoing throughout the hallways. What do you think? Also if you think it's the lord's castle, how long would the griffin have to be occupying it before you would call it the griffin's castle?
I'd suggest there are two competing priorities - realism and reader comprehension. If the storyworld was authentically portrayed, there would be a messy handover with some people calling it one thing and others calling it another, and lots of correcting themselves. Just as happens with a shopping centre's or street's name being changed. But in a story, this risks confusing the reader. It's probably safer to give it another name that can stay the same all the way through so that the location can be established more easily. In a story a place is only its name - there isn't an actual castle in the background that we can point at to help the reader.
I would say that a lot depends on where you want the reader's sympathy to lie, and possibly what happens in the end. If you want us to sympathise with the Lord whose castle has been occupied and will ultimately be reclaimed, it's more the Lord's castle. If the Lord was a complete arse and the locals are going to prefer having a griffin around the place, then it's the griffin's castle. Failing that name it after the nearest town and keep it that way.
The CCP still calls Taiwan a province of their own, the Kingdom of Siam went centuries before they declared "Yeah actually call us by our real name" and Crimea is occupied by Russia but identified as the Ukraine on most maps. Not even mentioning anything Balkans-related here - de jure acceptance depends heavily on diplomacy and politics. What I can think of is Erebor here; the Dwarves stuck to calling it Erebor & the Lonely Mountain for years. Clinging to it gave them power and hope, and no dwarf of decent stature would have acknowledged it as "Smaug's Lair" - in fact, I'm sure most of the Erebor dwarves would erupt for a brawl as soon as Erebor was called a dragon's lair. After a few weeks, definitely Lord's castle. Even after a year or so. I imagine the Lord's allies and some adventurers would launch a few attempts to reclaim it. When they all fail and the Griffon's hold solidifies, and when people give up hope that those within the tower might be freed one day (or even hope they're still alive), they'd accept a new name. "Lord's Castle Ruins" or "Gryphon Rock" or "Castle Roosts".
This is one of those “how long is a piece of string?” questions. Or maybe “how many grains of sand make a heap?” If the griffin demands that people call it “The Griffin’s Castle” on pain of death then I guess that would be pretty quick. If you mean that the name changes naturally over time, then that could be never. I can think of many locations near where I live that have names that have outlived the building that was there. The Hen and Chickens is still an area near me, despite the fact that the pub closed in the early 90s, but people who never knew it still refer to that junction as Hen and Chickens. They may never call it Griffin’s Castle. They may just call it The Castle (unless there are multiple and they need to differentiate). You may even want to consider if they’d call it the Lord’s castle at all. Would they need to point out who it belongs to?
You could just give the castle a name and leave it at that. Like Leeds Castle or Arundel Castle. Sorry in advance but most of the ones I know are from the old game Kingmaker
I would call it the Lord's Castle until the point that he leaves and will not come back, leaving it to the Griffin's.
