The passenger names listed in your email confirmation are the names that were ticketed. Viewing the reservation in the My Trips portion of your RR account does not include the middle name. That is a rather odd discrepency.
I can't check right now, but you may want to try viewing the reservation at https://www.southwest.com/air/manage-reservation/index.html to see if that provides a different result. If your email is correct then you don't have anything to worry about.
--TheMiddleSeat
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