Her father's gravestone at the Garfield cemetery gave his name as J.J. and says they came from Lommersum. The place would have been under the French when he was born, accounting for the name Jean Dorweiller that was given to him at his baptism The famed French ruler called Napoleon lost control in 1813. Control was then given to Prussian outsiders, with spellings shifting to a more north Germanic dialect. Her father then became Johann Joseph Dorweiler for his wedding to Anna Margaretha Dorweiler at Lommersum , the two using those spellings in all baptism/birth records for their children, all done in Lommrsum. The records included this daughter, whose stone seems to use her baptismal date, a day later than her birth.

Her father used his middle name Joseph Dorweiler when filing his homestead claim for his land in Kossuth County, down in Fort Dodge, late in 1872. This would avoid confusion with the too many called Johann/John.
Her older brother Paul Dorweiler filed at the same time, for land in the same township. This daughter adopted the same strategy, too many Annas, so used her middle name as her first, but Irish-ized the spelling of Catharina into Katharine.

The Bonnstetters had arrived earlier than her father in Kossuth County. Spouse Michael's biography in an old Kossuth County history, indicated they came circa 1865, while her brother-in-law Henry, a teen at the time, remembered 1866 when asked for his biographies.

Her married brother Phil would come from Guttenberg, Iowa, to file early in 1873 for added land at Fort Dodge under the Homestead Act, in the same township as her father and brother Paul, todays modern Garfield Twp., whose western edge overlaps with West Bend's 10th Ave.
Her spouse decided to claim some homestead land as well. Both surnames were wrongly spelled in the land records, but they now had land near her parents.

Her original name of Anna Catharina honored the wife of her uncle Anton in Clayton County and her mother's mother, as they were also Anna Catharinas. She must have remembered ties to the French, however, as Anna turned in to Antoinette relatively late in her Kossuth County records, maybe the idea of one of her children
.

[Research at FamilySearch and in county histories by Findagrave member JBrown, 2021, whose paternal ancestors were the Alexander Browns in Cresco Twp. and, on her mother's side, an Arndorfer who was a brother to the one marrying Katharine's niece, Paulene/Pauline Dorweiler. Pauline was said to be the first baby baptized at the West Bend church.]
Contributor: JBrown, IA, MN, Calif, AustinTX (48697180)

FindaGrave rules say to use the stone's date then explain any differences in the Bio section. A typed summary of her birth record is here, a day earlier than shown on her stone:

SOURCE: Familysearch.org/ark:/61903/1:1:NGLP-VQ2
Contributor: JBrown, IA, MN, Calif, AustinTX (48697180)