It's only that thepetitionsite.com works that way, you can check not to have your name displayed. It's a general petiton site, they won't forward your name to the GB
1000 signatures is nothing I'm afraid, especially if they come from an online petition. Not that any amount of signatures would do anything, but I bet if there was a paper list of signatures in order of ten thousands, the GB would at least have a discussion about it. .....then they would decide the control needs to be tightened, some are slipping.