I am taking lessons in Southern California (KSMO to be precise). When holding short of the runway before departure, we say "Santa Monica Tower, N643JK holding short of runway 21, Left Closed Traffic". This is equivalent to requesting take-off to remain in the pattern, which happens to be a left pattern at KSMO. Nothing special about that pattern, it's the normal large box rectangular pattern. You can also just say "Closed Traffic" if you're not sure of the direction of the pattern and tower will respond with "...Left Closed Traffic approved, Runway 21, Cleared for take-off". For the more unusual airports where the pattern in on the right, you would ask for "Right Closed Traffic".
I assumed these were universal standards but I now realize that VFR communication standards can vary by region. Not sure if this applies to everywhere in the US or just the West coast. This style is also recommended by PilotEdge (https://www.pilotedge.net/pages/cat-03-rating).
Another thing my flight school recommends doing at our airport that confuses Pilot2ATC is to ask for VFR flight following at the same time as asking for taxi to the runway:
"Santa Monica Ground, N643JK at south parking, request taxi to run-up B5 with information Lima, and request flight following to Malibu".
Then ground would first give directions to taxi to the run-up and a little later, while we taxi, give us a squawk code and departure frequency for the flight following. I realize this would be more complex to handle for the AI and it's not a big deal to break it up in two separate requests.