The name derives from the word dove house. The dovecotes, whose furnishings belonged to the privileges of the nobility, were often in the open air. The huts of the vineyard keepers are referred to here as a dovecote.
The name of the singular is due to the unusually high sum as an expression of general appreciation to watch. It may even be that here is the actual purchase price.
The location was mentioned in 1303 with the name "amme Steynwingarten". The name Steinert was created by the contraction and refers to the soil quality.