"remain in pattern" works just as well.
Pilot: "Tower, Cessna 123AB to land, full stop."
Tower: "Cleared to Land number 2, winds 210 at 6kts"
At smaller, single runway D's tower will either ask what you want, or wait for you to tell him and keep you on his frequency. At Santa Monica it goes like this:
Pilot: "Tower, 3AB taxi back 21"
Either with ground or tower, all you need to say is where you want to go.
When holding short:
"Tower, Cessna 123AB, short 2-1 ready to go Left/Right closed traffic."
Tower will then assume you want the option for each circuit, and give you instructions to either report midfield, or may just call you at his leisure (always a good idea to report midfield anyway). If you need to change it up, let the tower know next downwind.
"Tower, 3AB would like full stop"
"Tower, 3AB touch and go"
"Tower, 3AB after touch and go, left/right downwind/crosswind departure to the [direction]"
(At Santa Monica we have a local op, "right turn at the shoreline" which works, e.g. "Tower, 3AB would like right turn at the shoreline after this touch and go"
It REALLY is as simple as you though. The phraseology is "closed traffic"
(Remember, this gets more complicated if you made a full stop at a class C airport - be sure to check all your local noise procedures and common routes)