In The Lion, the Witch and the Wardrobe, what did Aslan mean when he said "All names will soon be restored to their proper owners"?

When we consider the meaning of given quotes it is
important to read them in the context of the entire novel. Aslan says this important
quote in Chapter Thirteen, just after Edmund has been rescued from the hands of the
White Witch. The Witch's dwarf comes to Aslan's camp demanding audience on behalf of his
mistress, saying rather formally:

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"The Queen of Narnia and Empress of the Lone
Islands desires a safe conduct to come and speak with
you..."

In response to this
recitation of the titles that the Queen feels she has a right to, Mr. Beaver expresses
his annoyance that she calls herself "Queen of Narnia." It is then that Aslan delivers
the line you have picked out. This line indicates that Narnia is not running the way
that it should be and that the natural order of events has been disrupted thanks to the
White Witch and her tyranny. However, it also indicates that this is fortunately going
to be just a temporary state of affairs, and that Aslan will restore order soon,
restoring the "name" of Queen of Narnia to its proper owners - Susan, and of course
Lucy.