In layout mode, when you click on the portal (not a field or other object in the portal) do you see NamePortalSeach appear in the name box of the Inspector's position tab?
What user and/or script actions take place before the go to object step?
In layout mode, the name of the portal in the position tab has been named NamePortalSearch so that should work fine in my Go to Object step.
The full script is:
If [Name::kfTempName =/ ""] **note that =/ denotes a not equal sign here**
Enter Find Mode
Set Field [Name::LastName;"==" & Name::kfTempName]
Set error capture [On]
Perform Find 
Go to Object [ObjectName: "NamePortalSearch"]
Go to Portal Row [Select; First]
In the script debugger, I see the first row of the portal get highlighted but that record does not remain the active record when the script ends.
Doh... I figured out the error in my portal and layout. My portal was for the table "Name2" in my layout for the table "Name". I merely needed to add after the Go To portal [Select; First] script line a Go To Related RFecord [From Table "Name2"; Using Layout <current layout>]. Now it works as desired.