You cannot ask the county to do anything without adding it to a deed. You will have to bring the deed (quit claim deed complete) with you and register it yourtself wihtout cost except for recording costs approx $25
The only way to do it is quit claim deed which you can prepare yourself. or have an attorney do it for you for a cost approx $100
But to go add a name by just going to the county office will not do it.
Not sure why you wont do a quit claim deed.. It's shows ownership only.
Reality if it is your main home it is Joint tenants anyway by NJ law. even without the spouse name on deed.
information here is not intended to legal advice.
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