After some guys here reported that new company name is a separate legal entity, I've submitted another application to AdSense with the same Contact Name and physical address. And got a response: So, you can't have another business account unless you provide a different contact name.
Unless you were banned, why did you want to get a separate adsense account? Were you concerned that you wouldn't have the right to put adsense on ads belonging to the company?
I own two different business accounts + my personal account. Each account is by itself, this way I can easily track and correctly file my taxes. Peace,