How can I get a judgement that is not mine removed.

I recently remarried and went to DMV for a name change apparently a collection agency uses DMV records to locate people. I received a bill from them for $1,735.00 for a judgement from the Superior Court. I immediately went to the courts website and entered my name. There is a judgement for a women with my exact name but it is not me.
It is for child support due in a divorce dating back to 1981. I have the case # and all the information. I called the collection agency and they told me it was my responsibility to clear this myself with the court. When I contacted the court they told me I need to get a lawyer. If you enter my entire name, first middle and last on people search there is about 75 different people with the same name. How can they do this? Your social security # is on file with DMV you would think they would check this. This is very stressful and apparently they can suspend my drivers license if this is not cleared up.