How do I request a touch and go and then remain closed traffic? When I first contact a tower to request touch-and-go, if I want to remain closed traffic after the touch-and-go, can I say 
'...tower, call sign, location, inbound for touch-and-go and remain closed traffic'?

I learned touch-and-go yesterday and I'm a student pilot in the US.
Yes you can request that on your call, generally if you don't the tower will ask how you will terminate/proceed at which point you will request closed traffic.