What were the rules or conventions for choosing the name of a new dynasty chosen? Was there a single method for naming all of the Chinese dynasties?
There are no specific rules, it is completely up to the founders. Many dynasties ultimately took their names from one of the ancient states of China. In any case, usually the actual choice were made in one of six ways:
Reviving an Ancient Name: the dynasty began where an ancient state existed, and took its name from its ancient predecessor. Examples include the Former Song, whose founder's family had lived on the ancestral lands of the Song state for generations. This is probably the most common type, due to the situation described in #3 below.
Place of Origin: the dynasty took its name from the name of the location it started at. More often used by nomadic dynasties; for example, Liao and Jin were founded by tribes hailing from the banks of the rivers Liao and Jin, respectively (alternative theory is they were named after the metals). In some cases the location name was also derived from an ancient state name, such as Song. Its founder was the military governor of Shangqiu, the ancient capital of the Song State; the city was also named Song at the time.
Previous Title: a twist on the previous two types; the dynasty's founder previous held a lower title (typically king or duke), and kept the name when upgrading to emperor tier. Examples include Han, whose founder was made King of Hanzhong by Xiang Yu. The Sui and Tang dynasties were founded by the Dukes of Sui and Tang, respectively. The original title is typically derived from the location, à la the previous two cases.
Ancestral Name: a previous member of the clan (i.e., sharing the same surname) had founded an illustrious dynasty; and the new upstart chose the same name. Often there is no actual family link whatsoever, and this was instead a political strategy for shoring up legitimacy. Examples include the Later Tang, founded by a nomad whose ancestor was given the royal surname. Legitimate examples include the Eastern Han, whose founder was descended from a minor branch of the Han Dynasty ruling house.
- Made up on the Spot: sometimes a dynasty's founder simply came up with a catchy name he likes for some random reason. Examples include Qing, which was renamed from Jin by its second emperor for no apparent reason (there are unsubstantiated theories). Another is Mongolian Yuan, which was apparently named after a phrase in the divinations book I Ching by the fifth Khagan of the Mongol Empire.
- Surname: when the dynasty is named after the surname of an exceptionally egoistical founder. Only ever happened once, with Chen. It didn't last.
Origin of Qing's Name
There's five theories I know of:
- It is a better looking character for transcribing the same name. The previous character, Jin, was already used by the fallen Jin Dynasty, an earlier Jurchen state originating from Manchuria.
- It symbolically makes the Manchu state equal to the Ming Empire. Both Qing
(明)can mean "clear".
- It fits the Cycle of the Five Elements theory. The Ming Empire was Fire; the word Qing
(清)contains a water radical (the three dot-strokes on the left). Hong Taiji chose it to symbolise putting out the fire of Ming.
- The Manchurian liked the colour blue (sky?) due to their Shamanistic beliefs. Blue (
青) is the same word as Qing
(清)minus the water radicals. This ties in with the previous theory.
- It was a transcription of a Mongolian word meaning something along the lines of "good fighter".