Yes, I guess in most of Europe the 200-250 years between Rembrandt and van Gogh is exactly when family names solidified from a simple description "the one from village X" or "son of Y" or "the one with a red hair" to become a hereditary name essentially detached from its meaning.
Also, van Gogh's popularity came from France, the work he did in France, and in France by this time family names had been standard there for a long time already (since around the 16th century), much earlier than in the Netherlands.