Beebe: I am a Real Estate Broker, not a lawyer. To be honest, I don't even know what a "Deed of Trust" is. A deed is a conveyance. It says that the grantor alienates the property in favor of the grantee. It is a legal document and must be produced by an attorney. Individuals may be able to generate their own deeds but I know for sure that Licensed Real Estate people cannot do this.
Once a deed is passed between parties, it is usually filed at the County in which the property is located. This filing is done in the county clerk's office. If the deed is not filed, the last filed deed will be the indication of ownership and the party to whom property tax bills are sent.
Therefore, "adding" a name to a deed would mean a conveyance to additional owner(s.) I would assume that the deed would have to be generated by an attorney and then filed. Obviously, if you have pledged the property as security for a loan, the lender will have a great deal to say about any change in the ownership and therefore the deed. This may be "fixed" by simply adding the new owner to the mortgage. On the other hand, it may be that the lender will not accept an additional owner under any circumstances.
The bottom line in all this is that you need legal advice and you need to clear any change in ownership with anyone to whom you have made any security pledge or who has an equitable interest in the property. You should start there, not with a Realtor.