|It depends. Definitely an answer you want documented from whoever hired you - title insurance company and/or lender.|
Do this a lot and the answer changes with the circumstances and what the "higher authority" wants. Often Trusts do not have liquid funds to repay the loan, BUT do have the assets to secure the loan.
Signing instructions, I've experienced:
Sign twice everywhere: Name and Name, Trustee
Sign twice on X, X and X: Name and Name, Trustee
Sign Only on Note: Name
Sign Only on Mortgage Deed: Name, Trustee
Sign Only on X, X and X: Name
It reads like the closer preparing the documents did not have software (or a typewriter to modify THE FORM) to meet the specific circumstances of the loan and borrower(s). Not to complicate, but you definitely want to document what you are told to do. Doing it not the way lender/title company wants can come back to bite you for FREE fixes months after documents are signed ... or a mad rush to fix it yesterday. Good luck - excellent learning experience.