OP - it's not clear if you still work for somebody and you are getting insurance through a job, or you are buying insurance in the private market or the marketplace?
Generally speaking in both terms of size of insurance company and also in size of national network, you'll want to consider the 4 big ones:
Blue Cross Blue Shield (as mentioned above). They have regional partners with agreements to cooperate with one another nationally.
UnitedHealthcare
CIGNA
Aetna
However, if you are buying insurance on the marketplace, these national players are pulling out of many markets due to poor financial returns on ACA marketplace. They just can't squeeze out a profit. Each also has a menu of 'networks' and you'll want to pay attention to exactly which network you are gaining access to if you buy into their plan. Some cheaper plans are intentionally narrowed into one regional network to reduce costs and you'd be paying out-of-network for any provider outside of this.