How do I rename my local SQL development server?
How to: Rename a Computer that Hosts a Stand-Alone Instance of SQL Server


Rename the computer.
Restart the computer - SQL Server will recognize the new name during startup, but the sys.servers table will still contain the old name (you can run SELECT @@SERVERNAME to confirm it).
Run the sp_dropserver and sp_addserver procedures to update this table.  

According to BOL, the former requires the ALTER ANY LINKED SERVER permission and the latter - membership in the setupadmin server role; however, brief sp_helptext and Google investigation suggests that actually they both require this ALTER ... permission.
Restart SQL Server and use SELECT @@SERVERNAME to verify that the previous step has been successful.




Apart from technical considerations explained in the How to: Rename a Computer ... article (e.g. computers involved in replication cannot be renamed), the thing I would worry most about is finding and changing all the connection strings:  


the ones in app.config and web.config files,  
the ones hard-coded in some prototype applications,  
the ones hidden somewhere deep in configuration of SharePoint, Analysis Services and other systems,  
the ones embedded in Excel files or Access databases).