I'm not a TV expert so let's wait for the moderator who made the changes to respond, but on the official Netflix page it says: "The Haunting Continues in 2020". So maybe the series is called The Haunting and season 1 is The Haunting of Hill House, season 2 will be The Haunting of Bly Manor etc.

Yeah, I knew there'd be a good reason for the community to name it "The Haunting" instead of what I suggested. I'm just a new guy trying to figure out how this stuff works. Thanks for the reply.

That is my guess, but we can wait for a response anyhow. Thanks.

I changed the original title based on the fact that the series has been renewed and Netflix calls it an anthology series https://variety.com/2019/tv/news/haunting-of-hill-house-renewed-netflix-1203144815/

I had no idea that this was now a confirmed anthology series. I was confused because on IMDb and TheTVDb, it's listed as "The Haunting Of Hill House". Thanks for the clarification.

This seems like speculation. No official sources have said that is the new title. Just an interview where they could be speaking in shorthand. The Netflix page, IMDb, Wikipedia... They all say "The Haunting of Hill House"