Must I use the insurance company's designated repair shop?

Not mandatory.

Designated shop:
The process is usually faster and smoother, with convenient rental car arrangements.
You only pay the deductible (if any); the shop and insurance company settle directly.

Your choice:
You need to notify the insurance company first and wait for an adjuster to go to your chosen shop for damage assessment.
If the shop's quote is higher than the insurance company's estimate, you may need to pay the difference yourself.