There are usually many Deputy District Attorneys or prosecutors (a district attorney is a prosecutor). Normally if there was only one in a courthouse it would be a really small town or small courthouse. Many large cities/counties have over a hundred Deputy District Attorneys/prosecutors working in many different divisions (based on types of crimes, locations, etc). A case can be switched to a different District Attorney or prosecutor - it happens all the time.
There is only District Attorney in L.A. County. He has many Deputy District Attorneys that prosecute the cases. A prosecutor and a District Attorney or Deputy District Attorney are one and the same. Most courts in L.A. have many prosecutors / Deputy District Attorney.
The prosecutors can switch in the middle of a case...just like a defendant can hire a new defense attorney if they want.