I've given a fair bit of thought to the branding, and I'm fairly settled on the brand name being structured as "The Adjective Noun", which includes my generic keyword but adds and element of unique branding.

I'm not sure what to do with my domain name though.

Does it make sense to keep the "the", drop it or register both domains?

www.adjectivenoun.com
www.theadjectivenoun.com

What do users expect when typing in a domain - do they expect to type "the" if the company name starts with "the" or do they expect that it will be dropped? (Especially in names where the "the" is less essential ie "The Keg" relies heavily on both elements of the name, "The Davinci Code" might reasonably be referred to as "Davinci Code")

If I register both, what would be the best strategy for using them?

Or is this something that is going to cause me untold headaches down the line and rethinking the brand to eliminate "the" is the best solution at this point (I'm really quite content with the brand beyond this domain question.)