Mimino

I meant, in case you don't pay up. Either way, I'd have to tell him no. It sucks, but this whole situation makes me feel uneasy.

At this stage of the game you actually need to do an official name change through the courts. Submitting information to update your green card status isn't the route that will do this.
What you may wish to do, however, is if you plan on applying for Citizenship you can make any name changes at that time. The Naturalization document contains a section where it asks if you wish to change your name. As part of the Naturalization process, USCIS then submits the documentation to a judge who then makes the legal name change official, and then processes the Naturalization application in the new legal name. There is no additional fee for a name change as part of the Naturalization process, but there is one - several hundred dollars, I believe - for a legal name change otherwise.

compared to replacing a lost/stolen gc, those are a cake to replace. don't even mention the cost of a new gc...