Is it legal to sell a product and then buy it in the buyers name (forced dropshipping basically)?

It sounds like a good idea, but in my view point, buying under somebody else's name and using their details would be fraud. However, if you advertise the product elsewhere, such as ebay as you say, then define maybe a longer shipping period to the end customer, and then buy the item at the original price in YOUR name then forward it on, you are within all legal boundaries, as long as you are not infringing any copywrights or trademarks or patents...