This could be done if you enable 'Hide Bidder Details' in the submit auction page.

For this, login and click on Sell. Tick the following checkbox.

If anyone tries to view the Bid and Purchase History, he will get the message ‘Seller does not wish to disclose the details of the bidder.’

Also, in the item page, 'High Bidder' will be displayed as ‘Hidden’ in this case.