Need to remove a name off of the house deed of trust

Just to clarify, do you mean deed of trust, which is the mortgage instrument, or do you mean the deed that transferred titled?  If it's the former this has to be done with the mortgage company through a refinance.  If it's the latter, the persons named as owner(s) in the deed simply execute and record another deed to the person or persons who are to remain owners, removing the other(s).