Maybe the DPD didn't take Kim's name because they are familiar with the AV. They picked her up drunk, half dressed, and minus a six inch white shoe.
Keep in mind that Kim changed clothes in the bathroom before they left the house. This tells me that she either had plans to go somewhere else (besides home) after leaving OR that she knew in advance she would have to be having contact with the cops in order to dump Mangum and did not want to be dressed in stripper's garb such that the cops would make a connection between them.