As per my personal observation/suggestion, Its much better reinstall server again with new name and then detached DBs from OLD instance and Attach with NEW Instance, because a instance name is associated so many things like performance counters, local groups for service start and file ACLs, service names for SQL and related (agent, full text) services, SQL browser visibility, service master key encryption, various full-text settings, registry keys, ‘local’ linked server etc. Although, we can change Name as following the below steps,
— For default instance
sp_dropserver ‘old_name’
go
sp_addserver ‘new_name’,‘local’
go
— For named instance
sp_dropserver ‘Server Name\old_Instance_name’
go
sp_addserver ‘ServerName\New Instance Name’,‘local’
go
Verify sql server instance configuration by running below queries
sp_helpserver
and then restarted the SQL server with following command at command prompt J
net stop MSSQLServerServiceName
net start MSSQLServerServiceName