If its the same user with a changed user ID, yes there is a way to find out. You can check out his user profile and see if there is an ID change recently. If there has been no change, you can request from ebay the bidders user info, but only if they have bid on your items. Since they bid they are in a biding contract with you if they win, so this allows you to request their personal information from ebay. If it is the same person, but using a new ID (as opposed to an old ID with just a name change) you have the rights to cancel any and all of their bids on your items, and also you can block their ID from future bidding on any of your items.

If you have them blocked as a bidder under their old id. The new id will not circumvent that block.

This is true, however, if they have created a totally NEW account, they will not be blocked. It's very easy to create a new ebay account and throw away the old one when things go bad.

Ah, very true.