Excellent question. I'm betting each school could set it to what it prefers. Ds's number was his current GPA, but I haven't gone back to check if that number has changed (it went up senior year).
Our kids' schools changed the GPAs every semester. Also changed SAT scores, but don't recall if that was on a semester basis too, or if they did it every time the school got a new wave of scores.
^Ours does change the SAT scores if appropriate and I think they change GPA once actually from the spring junior year GPA to the one they give out in the fall.
S2's school also loaded PSAT scores until there were SAT scores. I recall that S2's sophomore PSAT score was on Naviance when he first got his account early junior year. Switched to junior PSAT in January, and SATs.