Script to get Linked server list. We have repeated linked server name if it has more than one associated remote login.

 1
 2SELECT @@SERVERNAME AS 'Server Name'
 3,      sys.servers.server_id AS 'IdLinkedServer'
 4,      sys.servers.name AS 'Linked Server Name'
 5,      CASE sys.servers.Server_id WHEN 0 THEN 'Current Server'
 6                                         ELSE 'Remote Server' END AS 'Server '
 7,      sys.servers.product
 8,      sys.servers.provider
 9,      sys.servers.data_source
10,      sys.servers.catalog
11,      CASE sys.linked_logins.uses_self_credential WHEN 1 THEN 'Uses Self Credentials'
12                                                          ELSE sys.server_principals.name END AS 'Local Login '
13,      sys.linked_logins.remote_name AS 'Remote Login Name'
14,      CASE sys.servers.is_rpc_out_enabled WHEN 1 THEN 'True'
15                                                  ELSE 'False' END AS 'RPC Out Enabled'
16,      CASE sys.servers.is_data_access_enabled WHEN 1 THEN 'True'
17                                                      ELSE 'False' END AS 'Data Access Enabled'
18,      sys.servers.modify_date
19FROM            sys.servers
20LEFT OUTER JOIN sys.linked_logins     ON sys.servers.server_id = sys.linked_logins.server_id
21LEFT OUTER JOIN sys.server_principals ON sys.server_principals.principal_id = sys.linked_logins.local_principal_id

Source: https://gallery.technet.microsoft.com/scriptcenter/Get-List-of-Linked-Server-d6c95d9c