"A whole new site."
Says it all. If it's a whole new site to you,how do you think Google will see it? Yup, got it in one.
You have choices; make changes in design and content, but, where possible, keep the main site structure the same, at least at first, and gradually update that (if it needs it), over a period. This allows Google to assimilate new content, rather than change wholesale.
Another possibility is to not remove any of the old site (yet), just add the new, and place the links to the old less prominently (but be careful, and be sure they are HTML). Again, once the new stuff has been assimilated, remove the old.
If the old really has got to go, then go it must. But use 301 permanent redirects wherever possible from 'old' sections to 'new'. This may reduce the time the site drops, and the amounnt of drop that it suffers.
But a new site is a new site.
Renamed page, to Google = one page removed, one new one added.
And a new page is a new page.
Plan the move very, very carefully, and stage it if at all possible.