"Judy does not have a brown and blue coat."
Translation:لَيْسَ عِنْد جودي مِعْطَف بُنِّيّ وَأَزْرَق.
عند means at or by. Therefore, like how in English you don't say "Judy she has...", in Arabic you don't need to say "عندها جودي...". Do note, however, that in dialect and less formal MSA, the common structure would be "جودي عندها..."