As long as the BlackBerry Server logical name stays the same you are OK using a different hostname. When you install the BES it picks up the NETBIOS name of the server you are installing on in one of the install screens and you can simply change this to the BlackBerry server name that you want it to be. (The BlackBerry Server logical name is the one that is next to the green icon in the BlackBerry management console).
In order to move users you need two SRP's and both servers need to be pointing to the same configuration database for the move to be seemless. I.E. the 2nd server will send out its service books and assume control of the user.
Here's a method I use sometime when migrating BES's.
1. Get a second SRP ( these are easy to come by these days by simply getting a PIN code from one of your devices and going to BlackBerry
2. Set up a 2nd BESAdmin user/mailbox in Exchange
3. Give your current BES Admin account full rights over this new mailbox
4. Log in using the original BES Admin acount on the new server and install a 2nd BES with the SAME
BES logical name as the other server but using the 2nd SRP, pointing the the 2nd BES Admin mailbox and a different configuration database.
4. Add a test user and make sure everything works OK
5. At the point of cutover turn off BES 1 (and set the services to disabled), move the database so that BES 2 can use it, repoint BES 2 MAPI profile to use the original BES Admin account and the server config settings to the moved database and hey presto........ The new BES thinks it's actually the original BES and uses the original SRP and has all your IT policies and MDS settings etc.
Just don't turn the original back on again....!!!!
OK, so you need a 2nd SRP to get the 2nd BES installed and tested but if done properly your actual downtime is as little and 5 minutes. It also means that you don't actually add the users to the 2nd BES and then back again. They always belong to the original BES.
I've used this method on a BES with over 500 users and it works a treat.
There are other methods of course so if this one doesn't suit then tell us what you would prefer and we can help.