Yeah, I tend to think that “neat” is a bit underwhelming unfortunately. That’s in terms of when people say something is “neat.” Not to say that having a “neat” home isn’t a goal. It’s just not a really good adjective to me.
Also, I am not a fan of having the hyphens in a URL, because people will mess that up often if they are actually trying to type it in.
I looked up “Tidy Home” on USPTO, and it looks like you could probably get that Trademark as there is only one LIVE trademark with that name, and it is a cleaning service somewhere in the U.S. They are not selling products.
Also, “www.ThisTidyHome.com” is available (most other combos are not).
I am not GUARANTEEING that you can get this name trademarked, but it looks like it could be possible.