every GC i've worked for sends 1099's;...this can help determine wether the check will be cashed or deposited.
It does not matter how you handle the payment, the agency will be sending the 1099 and they don't care what you do with the payment. Any and all tax liabilities are the responsibility of the recipient.
I guess it really only becomes a problem if you are audited and your records don't match the 1099.
I know of no bank that will cash a check made out to a Company.