李 is the most common Chinese surname, shared by over 100 million people. Famous Lis include poet 李白 (Li Bai), martial artist 李小龙 (Bruce Lee), and multiple Chinese emperors.
Top indexing tree radical 木 - anchors 李 in the tree/fruit domain. The plum tree is the original referent. Same family as 桃 (peach), 杏 (apricot), 梨 (pear). The tree above the fruit-bearing element is a classic fruit-character pattern.
Bottom 子 - represents the fruit or seed of the tree above. 子 in this context means the small offspring of the tree, i.e. the plums. Tree producing fruit-seeds = plum tree. The surname use is purely a borrowing of this character to write a clan name.
