Playstation 5 bill valid on another name?

And although I want to buy a Playstation 5 (ebay), it is often written that a bill is available, but I ask myself whether the bill will bring me anything. (Guarantee)

The guarantee runs on a different name, would it still be possible to use the Playstation 5 at e.g. To send back a defect or for repair?

The bill is usually only intended to prove that it is real.

Yes, the invoice is only valid as proof of purchase for the market / shop in which it was purchased. So you shouldn't have any problems with the invoice.