I own an LLC-based out of California in the bay area. While I own the basic domain for my company, I intend to launch my entity's first project using a different domain/name. That is, it's still owned and operated under the wing of my company, but the project name is not the same as the company name. Same is true for the domain. e.g., MyCompany.com vs MyProduct.com.
I don't know if this effects anything, but the project's monetization is affiliated-based... Simply sending leads.
Edit: Just to clarify a little more, I intend to release numerous projects under the LLC, each with different names. Just starting out with this first project though :)