Execute stored procedure in another server from sql agent job
As the error message suggests, OPENQUERY looks for a linked server.  If you don't have that set up, and don't have the rights to get that set up, then perhaps using an OPENROWSET query might be the way to go.  This will allow you to connect to a datasource on a more ad-hoc basis, by writing a query which contains a full connection string.

In your case, you may get the results by using something like:

SELECT spresults.* 
FROM OPENROWSET('SQLNCLI', 'Server=1.1.1.1;Trusted_Connection=yes;',
                'EXEC [db_name].dbo.[sp_ProcName]') AS spresults


CAVEAT:  This will fail at runtime if your SP returns multiple resultsets.

CAVEAT 2: This will also fail if Ad Hoc queries haven't been allowed.  To sort that out, you need to run the appropriate sp_configure statement(s):

exec sp_configure 'show advanced options', 1
reconfigure
exec sp_configure 'ad hoc distributed queries', 1
reconfigure


Of course, in order to run sp_configure, you'll need the appropriate rights in SQL Server.  According to the "Permissions" section of the sp_configure documentation, that's "ALTER SETTINGS", which is by default part of the sysadmin and serveradmin roles, but may be assigned to other roles too.