Each database is owned by a server principal (aka login). Inside that database, the owning principal is known as
dbo (aka *D*ata*B*ase *O*wner). The database principal (aka user) loses its real name.
For example, for a database I own:
select user.name as UserName -- Database specific
, login.name as LoginName -- Server wide
from sys.databases d
join sys.database_principals as user
on login.sid = d.owner_sid
join sys.server_principals as login
on user.sid = d.owner_sid
Will print "dbo", "Andomar". If you'd change the owner to
exec sp_changedbowner 'sa'
The query would return "dbo", "sa".
You cannot modify the default schema for the user that owns a database. It is always user name
dbo with default schema name