I don’t know what was going on in George’s head, but I can make something up real quick.
WARNING: COMPLICATED AND STUPID MENTAL GYMNASTICS AHEAD
(ignoring the PT entirely)
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Anakin’s last name was originally Lars, but being “the best star pilot in the galaxy,” he earned the nickname/title Skywalker.
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Luke, not appreciating his nickname of Wormie, took the nickname he heard associated with his father because it’s much cooler.