Your assets should be titled in the name of the person or entity you want to control the asset. If, for example, you have a limited-liability company (LLC), assets to be controlled by the LLC should be owned by the LLC. Similarly, assets to be controlled under the terms of your living trust should be owned by the trust or have the trust named as a beneficiary or transfer-on-death beneficiary. Traditionally, the title to trust assets has been held in the name of the trustee or trustees of the trust, but Nevada law (NRS 0.039) recognizes a trust as a legal "person", and it is legal in Nevada to own assets in the name of the trust itself.
If property is insured and/or mortgaged, you should not transfer the property without first consulting with the insurance company and/or mortgage company to avoid creating problems.
For covered residential loans, federal law generally prevents a lender from enforcing a due-on-sale clause for a transfer into a living trust when the borrower remains a beneficiary and the transfer does not change occupancy rights. See 12 U.S.C. § 1701j–3(d)(8).
While a transfer of mortgaged property to a revocable trust is generally no problem, a transfer of mortgaged property to an LLC, partnership, corporation, or other business entity may allow the lender to call the loan due, forcing you to refinance the property or even disqualifying you from having a mortgage.
If you put insured property into a trust (such as a home or vehicle), contact your insurance agent to see if the policy needs a "rider" or other change to make sure that the trust is a proper "insured party".