There are so many things to point out here. Really sounds like you want to also check out some other forums like msexchange.org.
Firstly...your mailboxes are configured in AD to point to a specific mail server. In order to connect to the mailboxes, the exchange server name has to be the same as the original and I would not suggest doing that to test your DR.
If you want a good test. Create a closed network and restore a DC to it then setup to restore the exchange in it. This way you can test restoring a DC and Exchange server.
If you want to do a simple test to see how long it will take to restore your store and you have space on your exchange server to hold it, I would use the Recovery Storage Group. Good way to gauge store recovery and test to see if the mailboxes recover.
But as far as your steps go...
1. Install same OS and SP with same server name
2. Place in domain
3. Install Exchange server with /disasterrecovery switch (this installs all the binaries and retrieves configurations from the AD and sets the server ready to restore the store)
4. Restore store