The only thing I want to mention is that my method of not renaming the pages the same but different while you leave the old site up is conflicting with Sammy's advice.
What I did after publishing the new site design with all new page names was: In segments, republish pages of the new site design with the old page names as much as possible. For example I published all of the bio pages on one publish changing from the new to the old name so it replaced the old pages only in that section - leaving the rest of the new and old pages in tact. I waited a few weeks and then published all of the maps with the old name etc. and so on until after a while all of the old site design pages were replaced with the new site design pages. Occasionally I had a few "left over" old pages on the republish that no new page had been created to replace. I left those up until after all republishing was done with a large banner at the top stating it was left from an old version of the site to please click here to visit the new site pages. That then linked viewers to the index of what ever section the page had been in. I watched stats and saw it was working for me to transfer people to where they needed to be rather than lose them for having tried to visit a page that didn't exist or link to anything any more. I stripped those pages of anything but written content so spiders wouldn't try to crawl them any more.
I started from the less visited page groups and worked my way forward to the most visited pages over time. By doing this I never found much difference in the rankings. I think this was because cached pages still worked and web crawling never ceased to be deterred. It kept the whole thing from changing at once and caused less notation of change. I guess the spiders originally detected addition of content more than change so they kept doing their old job too.
Shoot, as if I know the inner workings of any given spider.
I just know the results were favorable and better than when I had previously made a completely drastic change from a site built on old software to a completely new site built on the new software. Honestly I saw dramatic differences even though content and meta tags still contained key words and in some cases content was merely copied. The codes were clean enough so it wasn't that.
I think this would work even if you rebuilt a site on the same old software but on a different file so it wasn't remembering past publishes to remove or update.
Anyway I think if your not going to try this method then I completely agree with Sammy's advice to rename the pages the same are in the old design as much as possible.