Macbook Air 2013 starts asking for name and password

It appears you purchased a used laptop which is still being managed by a previous owner. You can try contacting the Dover Public School's IT department to see if they can remove this laptop from their MDM (aka management system). It may be they forgot to remove it from their MDM, or perhaps this laptop was lost or stolen. If you just purchased this laptop, then I would return it for a full refund and avoid buying anything from that person/vendor since they did not properly prepare the laptop for sale.

There is no way for you to remove this management from this laptop.

Another potential danger of purchasing a used Mac is if a firmware lock is enabled since that a firmware lock is a security feature that requires proper proof of purchase so that Apple can remove a firmware lock, but people buying a used Mac won't have the proper proof of purchase acceptable by Apple (unless the Mac was purchased as refurbished from Apple or possibly an Apple authorized reseller).

FYI, when purchasing a used device, you should always perform a clean install of the OS by first erasing the drive before reinstalling the OS. This is to make sure there are no nasty surprises left behind by the previous owner and for a Mac to make sure there is no firmware lock or remote management of the Mac.

that looks to be a school managed device - you need to enter their info. contact their IT dept if you do not know it.

How/where did you acquire that computer?