We have the Ximenez-Fatio House Museum in St. Augustine. The “Fatio” - which we pronounce FAYzhio - comes from Louisa Fatio, a 19th century owner during the 18th century building’s boarding house days. She was the daughter of Francis Philippe Fatio, who was born in London in the 18th century to Swiss parents. He was a businessman and moved to Florida during the British Period. He is buried in a place along the St Johns River known as Switzerland because there was a small Swiss immigrant community there.
I would assume he was a descendant or relative of Johannes, since it appears to have been an important family.
(We lived on Fatio Lane in Orange Park, across the river from Switzerland, FL).
Where we disagree on pronunciation might be due to “British” pronunciation.
(They’re big on the “short-A”)