One thing that I'm noting is that you seem to assume that Lews Therin did not want the name dragon.
I on the other hand think that he indeed did want it, and was proud to get the name, but as his madness struck, he comitted acts that was so much against the name Dragon, that he no longer lived up to it. Thus earning the name Kinslayer.
WoT If... Lews Therin Drove Himself Insane?
in Theory Blog
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One thing that I'm noting is that you seem to assume that Lews Therin did not want the name dragon.
I on the other hand think that he indeed did want it, and was proud to get the name, but as his madness struck, he comitted acts that was so much against the name Dragon, that he no longer lived up to it. Thus earning the name Kinslayer.
Just my 2 cents.