The German family name Rumreich is classified as being of personal name origin. When a name is derived from a personal name it is usually the name of the bearer's father or mother which is adopted and transformed into a fixed hereditary family name. This name is then proudly transmitted from generation to generation, occasionally altered orthographically or abbreviated providing a link between the living bearer of the surname and the original bearer of the eponymous personal name from which the surname derives its origin. In this instance, the family name Rumreich originated from a variant form of the old Germanic personal name "Rumerich," which was itself derived from the Old High German words "hruom," denoting fame or renown, and "rihhi," meaning "powerful" or "reigning." Hence, the personal name might be interpreted as "famous ruler" or "renowned leader." Variants of the surname Rumreich include Rumrich, Rumriech, Romrig, and Ruhmer. One of the earliest references to this name or to a variant is a record of one Georg Rumrich, who wed Anna Catarine Funke on 20 February 1727 in Wilsdruff, near Dresden. However, research is of course ongoing, and this name may have been documented even earlier than the date indicated above.

Onomastic research shows that fixed hereditary family names were first employed in Southern Germany in the twelfth century. This practice of adopting a distinguishing name which was retained from one generation to the next gradually expanded to include all German speaking areas. It was however not until the sixteenth century that we can categorically say that the vast majority of Germans bore family names that had been borne by their fathers.