The Marketplace search pulls it up as Droid Eye Lite by Christian Tschoepe. Once you install it, the lwp listing is Blue Droid Eye, animation by TeamNuc.
And so far, most of my apps have remembered me, with reasonable exception. I had to sign back into Fring and Seesmic, but I think that might have been it. Even World War remembered me with-out having to do anything.
Edit: Oh, I forgot to say this.
While I in the Verizon store, another guy came in with the Droid. When he heard me explain my problem to the guy at the counter, he said that his started out the same way. GPS was running slow, often timing out, an it was always getting force closes and running laggy. All of which mine has been doing for about a week. I was working through the process of uninstalling apps to see if one was causing it.
He just ignored his errors until he was locked out of Google. Google everything. Not just his email, but also Marketplace and about 3/4 of his apps. Now he has to jump through the hoops with Verizon and Google to try and get his account fixed. Granted, I just have his word that he didn't do anything to cause it, but you never know.
So let this serve as a warning. Always back your stuff up.