My family name has two spelling variants, which are alternating in the catholic church records I found. Many people in the village had my family name so we can immediately see the tendency, one priest would write spelling A, then another priest spelling B, but the next one would revert to spelling A, and so on, for the whole 19th century.
Even my great-grandfather who was born in 1892, after the German empire was stable, still has his birth record using variant "B", while only variant "A" has been used in the Army and his emmigration and his post-immigration life.
Today I do not think it is possible for people in Germany to have multiple spelling of their family names, at least not officially. I wonder at which point in history it became a requirement to have the family name to have a single, fixed, official orthography.