As long as the borrower is also the trustee of the trust (most of us are), then you can borrow in the name of your family or living trust.
The only requirement is that we get a copy of the trust to review to make sure that borrowing in the name of trust is not against the rules of the trust. If that’s good, then we are good.
Most banks make you come out of the trust. I have had clients who refinanced and were never put back into their trust, leaving them at risk. For more details, feel free to call me.