I bought a Uno on eBay. The seller sent a Mega.
If I kept the Mega, would I need to modify Uno code to have it work on the Mega?
Maybe, maybe not. Depends on the sketch you are running.
Well, you got more than your money's worth.
Generally, since a Mega has much more I/O, memory, etc. than an UNO, you can certainly run your UNO code. But some of the pin functions that existed on the UNO are on different pins on the Mega. You will need to examine the UNO code, figure out what pins are in use and for what functions (like SPI), and redefine those UNO pins to different pin numbers on the Mega, so that they align with the proper functions on the Mega.