I am having this same problem and I see that you posted yours two years ago. Southwest has not fixed the problem.
My child has two first names. Both names are listed on their Rapid Rewards account. But when I try to use travel funds, it will only match if I drop the 2nd first name. But then it doesn't match the Rapid Rewards account. I've tried contacting Southwest multiple times and it's a system limitation. There's nothing they can do. So on the Rapid Rewards account I ended up putting their two first names as one word and I don't like this since it's technically incorrect but that was our workaround.
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