I'm sure there will be a scene in one of the upcoming movies after Anakin becomes Vader that Obi-Wan and Yoda are forced to erase all memory of Skywalker references from the droids for safety's sake. This will take place around the time they split up the twins and go into hiding themselves. Otherwise there is the danger of one of them blurting out the truth of the Skywalker family secret at an inoppertune moment, and ruining the plans of the Jedis.
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