They're usually named after the fiefdoms of the founders, with some exceptions. The Zhou Dynasty was named for the hegemony of the State of Zhou. The Qin Dynasty is named after State of Qin, which conquered all the other states. The Han Dynasty's founder, Liu Bang, was the Prince of Hanzhong, and Han came from Hanzhong. Cao Cao was the Duke of Wei, so his Dynasty was called Wei. Sima Zhao's hometown was located in the historical State of Jin, so his Dynasty was called the Jin Dynasty. Yang Zhong was the Duke of Sui, Li Yuan was the Duke of Tang. Zhao Kuangyin was the military commander of the State of Song, so he named his dynasty Song. The Liao Dynasty was named for the Liao River in Manchuria (the Khitan people that founded the dynasty were based in Mongolia and Manchuria). The Tangut Western Xia was founded in State of Xia.

The Jurchen Jin Dynasty, Yuan, Ming, and Qing were a little different.

The name of the Jurchen Jin Dynasty has a couple of origin stories out there. One explanation is that it's named for Anchuhu River, which in the Jurchen language meant "gold." "Jin" means "gold" in the Han language (Chinese). Another story is that they wanted to one-up the Khitan Liao Dynasty with their name. "Khitan" meant "iron" in the Khitan language. After defeating the Khitans, Wanyan Aguda (founding emperor of Jin) said that although iron is strong, it eventually rusts, and only gold is eternal.

According to wikipedia for Yuan:

The official title of the Dynasty, Da Yuan (Chinese: 大元, "Great Yuan"), originates from a Chinese classic text called I Ching, "大哉乾元" (dà zāi qián yuán), literally translating to 'Great is the Heavenly and Primal', with "qián" being the symbol of the Heaven, and the Emperor. Therefore, Yuan was the first dynasty in China to use Da (Chinese: 大, "Great") in its official title, as well as being the first dynasty to use a title that did not correspond to an ancient region in China."

The case for Da Ming (Great Ming) is a bit debated. Some say it's named for Ming Jiao (Manichaeism, the religion), others say it's taken out of the I Ching like Da Yuan. I'm not too sure about this one.

Da Qing is also debatable. There are a lot of different explanations out there but I don't know which ones are reliable. But it's definitely not based on any ancient fiefdom.