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In tracing the Jacobi/Jacoby/Jakoby surname, it appears that in at least two instances it was adopted by children of people with another surname.
Example 1: Hans Jacob Jacobi (1602-1676) was the third son of Andreas Niemeyer (1570-1624). Niemeyer's first two sons went by the surname Niemeyer, but his next two sons used the surname Jacobi. The available records don't indicate a second marriage, but there is a nine year interval between the second Niemeyer son and the first Jacobi son. There is a possibility that the Jacobi boys were stepsons.
Example 2: Jacob Jacobi (1660-unk) was the son of Jacob Wiecherding (1640-1678). He was the first son of Jacob, born two years after his marriage to Anna Frikkers. Wiecherding's remaining three sons went by their father's surname.
Possibly someone with a knowledge of 17th century Germany can offer some insight into these surname discontinuities.