Welcome to WebmasterWorld julianm
Do we assume you are going to replace example-example-example-example.com/example.html with example.com/example.html url for url?
No changes whatsoever to the files and extensions structure?
This is how I would do it, others will have differing opinions.
Upload the site to the new domain space, if it's on the same server even better, wait for the DNS to propagate if it is not already there and then re-direct from your registrar's control panel and point the old domain name at the new domain name.
Some control panels may want you to do both with and without www, some do both automatically.
Hey presto, old site on new domain name with all its backlinks intact and identical urls.
Ensure the new site is being seen everywhere and that direct type-ins to the old site go straight to the new site, when it does that delete the old site completely, do not leave any old files, references, whatever, otherwise your new site may just be seen as a duplicate.
but in that case I am wondering what happen with the current page rank and the fact that the longer name has special keywords?
Normally a direct replacement like this will retain all street credibility with all search engines, it may drop a little whilst they're sorting it out but usually this will be no more than a few weeks.
For best effect leave the old name pointing at the new name for as long as you can or until you are happy that the new site is ranking without its support.
Personally I would not change your index page titlebars for at least a couple of months or so until the SERPs have gotten used to your new name.