If one is paid under their SSN (Social Security Number) then reach out to the employer and correct any information returns they have (W-4, I-9, 1099, W-8BEN, etc). Sign the sheet replacing NAME with the TRUST NAME and sign NAME, TTEE (shorthand for Trustee) at the bottom.
As incentive, it's best to tell them one would like to sign as an Independent Contractor which would allow them to remove any benefits (health, dental, medical, etc.) they pay normally for an employee. Once paid into the trust, the company will typically send a W-4 or 1099 to the IRS on one's behalf - don't fight them on this point.
NOTE: The employer or their CPA should already be aware that money sent to an Independent Contractor is not subject to employment-tax withholding, a Independent Contractor is required to pay these taxes themselves (if owed).