Create Log Shipping Step Failed After ServerName Changed
So in SQL Server 2012 SP1 I did this:

EXEC msdb..sp_helptext 'sp_verify_jobstep';


I scanned for 14234 (the error number you received), and right above the relevant RAISERROR call, I saw this:

IF (@server IS NOT NULL) AND (NOT EXISTS (SELECT *
  FROM master.dbo.sysservers
  WHERE (UPPER(srvname) = UPPER(@server))))


So, run this code with a PRINT:

IF NOT EXISTS (SELECT *
  FROM master.dbo.sysservers
  WHERE (UPPER(srvname) = UPPER(N'ServerB')))
BEGIN
  PRINT 'Not found.';
END


Then verify exactly what is in master.dbo.sysservers and also check master.sys.servers. I suspect either those two views don't match or the name in both is not exactly ServerB. Show the actual syntax you used to call the procedure and verify that the server wasn't renamed with leading/trailing spaces, whitespace or other non-printing characters.

Another idea is to not use the system procedure to set up log shipping in the first place. Log shipping isn't all that cumbersome to set up and in the past I've always just set up the backup / restore jobs manually. Also the stored procedure you called first only takes monitor_server as a potential server name where it could get into trouble connecting somehow, and it is nullable. Are you sure you need to pass it? Why would you want the monitor server to be the same as the source server? If one goes down they're both down by definition. What happens when you don't explicitly name a server as the monitor_server and leave that and other related parameters null?

Also these various hooks and potential conflicts are why I don't ever bother to rename servers that are already running. I'd rather pay the extra cost of wiping, reinstalling and restoring than dealing with all of this after the fact - especially if the quick rename was sold as something "hassle-free."