Insurance Sent My Car to a Random Garage—Need Help!

So, I recently had an accident (my fault, I hit a parked car), and I contacted my insurance agent to sort things out. Instead of discussing repair options with me, he straight-up gave my number to some garage guy without even informing me. Today, this garage person called me, telling me he will do the "best repair" and that I shouldn't worry. He sounds confident, but honestly, I have no clue who he is or if I can trust him with my car.

I drive a 2021 Toyota Fortuner, and I've never had to repair it before—haven't even taken it to any garage for anything. So, now I’m stuck, unsure if I should just go with this guy or look for a better place. If anyone has recommendations for a good garage that uses high-quality parts and does proper repairs, please let me know!

Also, what should I be looking out for when handing my car over for repairs? Is there a risk of parts being swapped or stolen? Are there any red flags I should be aware of? Any advice from those who’ve been in a similar situation would be greatly appreciated!