While you can turn off incoming AirDrop, you can't disable sharing items over AirDrop to others on device. Most of the time, AirDrop recipients will be limited to the single AirDrop button (which can't be un-favourited from the ‘Apps’ share list), but if someone in your contacts is nearby with AirDrop turned on, they will likely show in the contacts section of the share sheet. This can't be configured on your device.
Configuration profiles can configure AirDrop access only on supervised devices.
If your device is supervised with Apple Configurator, you can install disable-airdrop.mobileconfig.