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 :)
Relax! There's nothing to stop you registering any ".com" domain name that you can find -- you don't need to have any association between your business name and the domain name.
You do want to include your company details in the whois data, however, and it is definitely a good idea to include the company name in the legal small print.
If you want to secure traffic to your site through an SSL certificate (for https:// traffic) then you must have your current company details listed in the whois record. You'll need to provide appropriate documentation when you purchase the SSL certificate -- registrars differ, but an example is here.