So, there's two parts to the answer to this question: First, why the names "Wei, Wu, Shu" to begin with? Second, why NOT the names "Cao, Sun, Liu" after the respective rulers of each state?

The names Wei, Wu, and Shu each refer to ancient states that occupied the rough area that corresponded to the area controlled by Cao Cao, Liu Bei, and Sun Quan. These states were prominent during the Spring and Autumn Period (771 to 476 BCE) and subsequent Warring States Period (475-221 BCE), two periods of history that had a significant influence on Chinese culture. There were many legends and famous events from these two periods, including some of ancient China's most well-known historical figures like Confucius, Mozi, King Wen, etc. By choosing names from this period, the rulers of the Three Kingdoms period were associating themselves with the prestige of an ancient state.

In Romance of the Three Kingdoms, Zhang Song introduces Yizhou, the area that will become Liu Bei's base of power, as "a name for the group of western counties and territories known of old as the state of Shu." The name "Shu" (蜀) comes from the ancient state centered on the Chengdu Plain, in modern day Sichuan Province, which was conquered by the State of Qin (秦) in 316 BCE. Qin would go on to become the first state to unify China. Later dynasties centered on this area that also took the name Shu include the Western Shu (405–413 CE), also known as Qiao Shu (譙蜀), a state founded by Qiao Zong, as well as Former Shu (Qianshu 前蜀, 907–925 CE) and Later Shu (Hou Shu 後蜀 , 934–965 CE), both during the Five Dynasties and Ten Kingdoms period.

The ancient state of Wei (魏) was located on the North China Plains, right where Cao Cao's center of power lay. When Cao Cao took the title of Duke, he had himself named Duke of Wei, which the story Romance of the Three Kingdoms ties to the Warring States period. In arguing for Cao Cao's ascension, Dong Zhao said, "In all history, no one has rendered such services as you have, O Prime Minister, not even Duke of Zhou or Lu Wang (another ancient figure). These thirty years you have exposed yourself to all risks, been combed by the wind and bathed by the rain, and you have swept evil from the empire, succored the distressed, and restored the Hans. Who of all statesmen can rank with you? It would be fitting for you to become the Duke of Wei and receive the Nine Dignities, that your merit and virtue be known to all." Later, he attained the title of Prince of Wei, and when Cao Pi ascended the throne, he named his new dynasty after the title he inherited from his father. Other Chinese states with this name include the short-lived Ran Wei ( 冉魏, 350-352 CE) state founded by Ran Min (冉闵) and the Tuoba states of Northern (386–535 CE), Western (535–557 CE) and Eastern Wei (534–550 CE), which ruled parts of North China in the Northern and Southern Dynasties period.

The state of Wu (吳) existed from the early 12th century BCE to 473 BCE, when it was absorbed by the neighboring state of Yue. Wu had a distinctive culture and language, which is one of the reasons the region maintained a distinct political identity even when controlled by others. Beyond the Kingdom of Wu founded by Sun Quan, there was also another short-lived state called Wu in the Ten Kingdoms period, sometimes called Southern Wu (Nanwu 南吳), or Yang Wu (楊吳) after its founder, Yang Xingmi.

So, why not name them after Cao Cao, Liu Bei, and Sun Quan? The simple answer is that this was not the practice in China. Dynasties were not typically named after the ruling family. Starting with the Qin Dynasty, which took its name from the geographic location the State of Qin, Chinese dynasties were typically named after a title, location, or sometimes even just made up. The state which preceded the Three Kingdoms era, the Han Dynasty, was ruled by the Liu family, for example. Sometimes the name of a ruler might be appended to the dynasty by later historians to distinguish it, as is the case with Yang Wu, Qiao Shu, and Ran Wei. Wei from the Three Kingdoms era is often referred to as Cao Wei (曹魏) to distinguish it, after the ruling family. Liu Bei's Shu is often called Shu-Han (蜀漢), reflecting Liu Bei's desire to portray himself as a legitimate successor to the Han, as opposed to Cao Pi, who proclaimed that "the Wei must replace the Han". However, all of these rulers would have simply referred to their own states at the time as simply "Wei", "Wu", or "Shu", as they were reviving the older title.

A lot of this information can be found in encyclopedias, but sources I used:

Ebrey, Patricia Buckley (1999). The Cambridge Illustrated History of China. Cambridge: Cambridge University Press

The Cambridge History of China.

Guangzhong, Luo. Romance of the Three Kingdoms.

The works of Rafe de Crespigny