Originally Posted by rollbread

Nope, have to write the agency name. They will definitely and confirm check on the records, if they can't find your name in the system they will ask for your pay slip to keep as record.

By then if you don't have the payslip or even worse they found out that you are lying, they might blacklist you in their organization.

Probably you can check with them to confirm first. Confirm with them whether you are employed under them or under the agency.