The Chinese imperial dynasties were typically named after their tribal origins, or after a prominent individual of the tribe/clan.

The Xia dynasty (2070 - 1600 BCE) was named after the Huaxia Tribe.

Shang dynasty (1600 - 1046 BCE) was named after the leader of the Shang tribe that overthrew the Xia.

Zhou (1046 - 221 BCE), again, the originating tribe was called the Zhou.

The split into Western and Eastern Zhou, was simply based on the location, within China, of their capital cities.

The Qin dynasty (221 - 206 BCE) came from a state established during the Warring States Period, that eventually overthrew Zhou - Again, named after the founding member and first leader of the Qin dynasty.

The Han dynasty (202 BCE - 220 CE) naming origins can be slightly misleading due to the ethnicity of most modern mainland Chinese people being Han Chinese. The 'Han' in 'Han dynasty', refers to the Han Kingdom which was located along the Han river in Southern China. It is because of the success of the Han dynasty period, after many centuries of upheaval, that Chinese people began to identify as 'People of Han' - simplified to 'Han Chinese'.

Moving on to the fall of the Han dynasty; the Three Kingdoms period (220 - 280 CE) involved three major players - all of which were named after either an honorific or a feudal title under the Han Empire (Wei, named after Cao Cao's title as Prince of Wei. Shu Han, named purposely to mean 'continuation of the Han dynasty in Shu/Sichuan', Liu Bei was related to the Han emperor thus was another factor. Wu, named after the Sun clan becoming Marquises of Wu.)

However, it is important to note that these were kingdoms and not empires - and more importantly, due to the chaos of the Three Kingdoms period, so many new titles were created. The Wei (via a coup d'etat by the Sima clan) eventually reached imperial status and created an imperial dynasty under the name of 'Jin'. This was because the founding member held the honorific of 'Prince (later King) of Jin' within the Kingdom of Wei/Cao Wei.

Thus dynastic naming convention remained relatively the same as previous eras, with naming the dynasty after origins of the tribe itself or after an individual of considerable merit.

I could go on listing more but they generally follow the above convention up until the 12th Century CE:

• Jurchen Jin (1125 - 1234 CE) was named after the Chinese word for 'gold'. However in English this looks identical to the previously mentioned Jin dynasty, but in Chinese characters, they are spelled differently - the 'Jurchen' part is to differentiate between the older Jin in English. The dynasty was named 'gold' because they overthrew the Khitan people, 'Khitan' meaning 'iron'... you can see why they would want to name themselves as such!
• Yuan (1271 - 1368 CE) originated from a phrase from a text named Yi, the phrase being; 'Everything Under The Vast Heaven'.
• Ming (1368 - 1644 CE) came from the religion of the founder named Manicheism, AKA Ming Jiao.

Finally we come to the Qing (1644 - 1911 CE), who were of Manchurian origin. Following the same idea that the Jurchen Jin had, the Qing named themselves as such because the surname of the Ming leaders was 'Zhu', if simplified - it means 'fire', or characteristics that are closely associated with fire. What is the best antidote to fire?... Water. 'Qing' literally means '(pure/clear) water'. In fact Manchuria had many rivers named Qing, before the existence of the dynasty.

The imperial lines ended with the Qing and an imperial dynasty has not existed since 1911.

I hope this provided some clarity regarding Chinese imperial naming conventions!

Edited Qing explanation after clarification was provided by u/EnclavedMicrostate