Schaub
A German surname likely formed from a nickname or emblematic word for “bundle of straw” or something similar.
The #5,749 most common surname in the United States (2010 Census) — about 1 in every 51,227 Americans shares it.
Etymology
The surname Schaub is generally linked in older German surname scholarship to the word for a bundle or sheaf of straw, rather than to a place-name or occupation. The historical excerpts you provided explicitly gloss Schaub as “bundle of straw,” which fits the common German pattern of surnames formed from everyday nouns and nicknames. The exact motivating image is not always certain, but the name is usually treated as descriptive rather than patronymic.
History
Schaub is found in German-speaking surname lists and has been in use as a family name for centuries. Like many short German surnames, it traveled with migration into other parts of Europe and later to North America, where it remains relatively uncommon but established. In older onomastic works it appears alongside related German names built from plain vocabulary items and nicknames.
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Fun fact
In one of the cited 19th-century surname lists, Schaub is glossed simply as “bundle of straw,” showing how everyday objects could become hereditary surnames.
From the historical record
“SCAUNI, brilliant, beautiful ; Schoner (Scauni -f hari). SCOCH, arrow; sing. st. ab., Schoch, Schick ; doub. st. ab., Schaub, Scheib ; dim. (1), Scheible. SiG, victory; Seybold, Seipel (Sig + bald); Seibert (Sig + beraht); Siegfried, Seyfert (Sig -f- frith); Sigafus (Sig + funs); Sieger”
— Studies in Pennsylvania German Family Names