big problem related to 404s and domain names

I had the web server launch my wordpress site recently, but for some reason it doesn’t show up on the first page after typing the name of the site into google search. In fact, the only thing related to my blog that DOES show up are a bunch of pages from the site from when it had a domain after it’s current URL (which I requested to be deleted from the launched site) that display a 404 error. Basically there are a bunch of pages of the prototype site floating all over the first several search results pages that shouldn’t be there. I talked to the web host technicians that launched the site and they basically said “that’s not uncommon”, and those links/search results will be moved back and the official one moved forward with time (about a 35-40 day cycle). Unfortunately, the person who was helping me with wordpress who created the domain name for me didn’t realize that the three initials after the last “/” are apparently an acronym owned by somebody else. So i might have a copyright issue here. Is there any way I can delete those remnants of the prototype site with the 404 error? Keep in mind that i called my web host and they basically said “those are there to stay”.