The Bank will require proof that the Company is a separate legal entity – this is called KYC ( Know Your Customer )and is a legal requirement – as they already know you this should be fairly straight forward. They will require the Certificate of Incorporation, a list of the directors and normally the ID docs ( passport/DL) for at least two directors , plus addresses and utility bills – all part of the anti-terrorisium act. If the company is listed on a public exchance then they may rely on that as evidence.
Note HSBC have just been fined USD 1bn for failing to due appropriate due diligence on companies and ended up banking some very nasty people
I work in banking, rather not say which one as you will all hate me.