Rapid Rewards points associated with flying, 6 points per dollar spent on a Wanna Get Away fare, are awarded to the individual flyer(s) actually doing the flying despite who pays for the ticket. Points earned from Southwest credit card spending are earned by the primary holder of the credit card.
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You will only get the points for your ticket. If you bought all the tickets with a Southwest credit card you would get the points for the money spent but for the flight credit each person flying would get there own credit.
If the others have rapid rewards accounts be sure to attach there number do they can get the points.
I continue to be surprised at how many people do not get a Rapid Rewards number on their very first flight. RR points are always good, even if you fly infrequently. Register your kids also. With or without the points the ease of buying tickets online or by phone is worth the small effort.