Is your company name a very unique name or something generic that a lot of other sites rank for? That makes it either very simple or more difficult depending.
SillySamantha'sCookies.com (easy)
FloridaPaintingContractors.com (more difficult)
I wouldn't do a subdomain or a new domain if you are trying to get #1 and #2 positions for your company name. I would optimize some additional internal pages for your company name on the main site and try to get the homepage and and an internal page ranked in the top two spots.