I need to know the name of the plug that goes into the gear shifter?

Hello, is this an electrical plug - wiring? Or is this a plastic trim piece of some sorts? Since you have a picture, seek a repair shop near you and show them - or drive your vehicle to them and ask for first hand advice! A good relationship with a local shop and technician is helpful for questions like this, and can often be consulted without charge, until hands on assessment and work is needed. Use this link to find some shops near you that can help with your concern: www.repairpal.com/repair-shops