If I am to copyright that name, am I entitled to that domain name or am I SOL?
If you look at the terms of the UDRP, for example:
[icann.org...]
it would seem difficult to prove the "bad faith" required element, as they'd have acquired the domain name before you even had any ability to create a trademark.
You might want to try buying the domain name from them, or renaming your company given it is very new.
Might be worth exploring a different company name....depending on its audience, etc. (esp. if you plan to have international clients).