I've read that in the United States, national forests, ranger offices, etc. often have some safety-related equipment for rent, such as bear canisters. Do they rent out Personal Locator Beacons, satellite phones, or similar equipment that can be used to call for help in the wild?
No, you can't rent that kind of equipment at a Park Service ranger station. They only rent out bear canisters, and even that is only at certain locations (e.g., Yosemite Valley). If you want a Spot or a PLB, you just need to buy one.