its uncommon to say an entire organization is a cost/profit center; instead you would say x department is a cost/profit center.
FWIW, i believe most insurance companies make their money from investing the insurance premiums - i would say within an insurance company the finance department is likely the profit center, and whichever department handles payouts to healthcare providers would be seen as a cost center for the org.
oh it may be worth adding- most major US insurance companies are run as non-profit organizations.