I believe that the boarding passes do have your name on it, however, in almost all the times I have flown SWA, the gate agent has simply collected the pass from the person, put it in a pile, and then scanned it after everyone in that particular line has boarded the plane.
As for saving seats, if your daughter is near the back of the plane she shouldn't have any problems. Problems arise when people start "saving" the prime seats such as the exit rows and the bulkheads. I flew back from Orlando once and encountered such a problem. A pre-boarding family got on and proceeded to save seats for the rest of their party(about 12 people with "C" passes) in the exit rows. They simply put their carryons on all of the seats. The flight attendant refused to do anything about it and there was a lot of grumbling from "A" pass passengers.
Keep in mind that the overhead space fills up quickly and passengers with "C's sometimes find there is no room for their luggage. On our last flight, the attendants were strictly enforcing the carry-on limit and checking any bags that they considered to be over-sized.
As for saving seats, if your daughter is near the back of the plane she shouldn't have any problems. Problems arise when people start "saving" the prime seats such as the exit rows and the bulkheads. I flew back from Orlando once and encountered such a problem. A pre-boarding family got on and proceeded to save seats for the rest of their party(about 12 people with "C" passes) in the exit rows. They simply put their carryons on all of the seats. The flight attendant refused to do anything about it and there was a lot of grumbling from "A" pass passengers.
Keep in mind that the overhead space fills up quickly and passengers with "C's sometimes find there is no room for their luggage. On our last flight, the attendants were strictly enforcing the carry-on limit and checking any bags that they considered to be over-sized.