Unfortunately, simply doing a factory reset on the device will not remove the previously connected iCloud account. This is done to prevent devices that someone finds to simply erase it and begin to use it.
You are likely going to need to complete an Activation Unlock, which requires original proof of purchase from the retailer you originally bought the iPhone from. Essentially, this process identifies you as the owner of the iPhone and will systematically remove the connected iCloud from the device.
You can submit the request online here: Activation Lock - Support (apple.com)
Since you mentioned that you have employees that have access to iPhones you own, you should reach out to Apple and inquire about MDM (Mobile Device Management) software. This allows you to always be in-control of company owned devices and you can reset them with a click of a button. If you are near an Apple store, call and ask to speak with the Business Team. They're local and solely interested in being a trusted partner for you and your business. See also: Business - Apple