Moving SQL Server instances from one datacenter to another
So the challenge here is to keep the server name, database name, and IP the same.

I've done this many times in the past without any issue. I always get another SQL Server built and get everything defined over on it as is currently on the SQL Server I'm migrating from such as linked servers, credentials, proxies, logins with matching sids and password hashes, SQL Agent jobs, and on and on. 

Be sure the Server OS on the new SQL Server has a "different" host name before installing SQL Server like ServerNameNew and a different IP Address, get the SQL objects defined or copied over (e.g. first paragraph above), tested and confirmed as best you can.

When it's time for the transition you will: 


Change the hostname and IP Address on the original server to
something different
Rename the new SQL Server OS to the original server host name
Assign the same IP Address(es) back to the NIC(s) on the new SQL Server
Change SQL meta data database name


  To rename a computer that hosts a stand-alone instance of SQL Server
  
  
  For a renamed computer that hosts a default instance of SQL Server, run the following procedures:
  
sp_dropserver &lt;old_name&gt;;   
GO   
sp_addserver &lt;new_name&gt;, local;   
GO

  
  
  Restart the instance of SQL Server.
  
  
  
  
  
  For a renamed computer that hosts a named instance of SQL Server, run the following procedures:
  
sp_dropserver &lt;old_name\instancename&gt;;  
GO  
sp_addserver &lt;new_name\instancename&gt;, local;  
GO  

  
  
  Restart the instance of SQL Server.
  
  
  source



If you get the new SQL Server built and define all the objects to match what's defined on the old SQL Server, and then test as much as you can until you feel comfortable with the testing results, make the changes as mentioned and everything should work as expected assuming you do not overlook anything in your test setup. 

Important: Have other people help test once you get the DB objects defined, etc. and run through your rounds of DBA testing or whatever. The more eyes and people testing the new setup, the better.   



Further Resources


Why are you still using sp_help_revlogin?
sp_help_revlogin (legacy)
SQL Server @@SERVERNAME returning old machine name?