Hello,
my SQL Server was installed with name 'FIRSTNAME'. After that I change its name into 'SECONDNAME', with :
sp_dropserver 'FIRSTNAME'
sp_addserver 'SECONDNAME', LOCAL.

But when I start:

select serverproperty('servername')

result is: 'FIRSTNAME'.

Wherefrom serverproperty('servername') takes information.

did you restart the server ?

Yes I did.

After restart @@servername shows 'SECONDNAME', but

select serverproperty('servername') shows 'FIRSTNAME'. So, it must be written somewhere that 'FIRSTNAME'.

did you also alter the physical servers name ?

     Jul 13  

Sometimes this is me

I did only sp_dropserver 'FIRSTNAME'

and sp_addserver 'SECONDNAME', LOCAL.

Nothing else.

I wonder where serverproperty('servername') gather information

don't mess with systemtables  

but how about :

select *
from master.dbo.sysservers

     Jul 13  

Sometimes this is me

name                         secondname

network_name           secondname

status                         rpc,rpc out,use remote collation     

id                               0

collation_name           NULL

connect_timeout         0

query_timeout            0