This is probably the most common surname in Chinese, and nobody ever cares about its meaning. "Kill"? This is my first time hearing about it. By the way my surname is Liu.
柳树 "Liu" Liu (third tone) means willow. The surname is 刘 or 劉 (fourth tone).According to http://en.wiktionary.org/wiki/%E5%8A%89 it originally meant "to kill". [noted -ed]