Demand that your insurance company pay for OEM parts
What's on OEM part? It stands for "original equipment manufacturer," and it means the parts are either built by the company that made your car, or by the same company that built them for the company that made your car. Generally speaking, the newer your car is, the easier it is to get the insurance company to capitulate, rather than springing for cheaply made parts that invariably don't fit quite as well.
If your car is new, request compensation for diminished value
What's diminished value? Let's say your car was hit pretty badly, but fixed so well that no one on the street or riding along would ever be able to tell. When you go to trade your car in, any inspector worth their salt will notice tell-tale signs of a collision, and offer you less money. To counter this, you can request compensation for that diminished value from the insurance company. This doesn't mean you'll get all of the loss, and it doesn't mean you're absolutely entitled to it if the damage was minor and fixed at a first-rate shop with OEM parts, but it's a good start.