Sui and Tang records, when speaking of famous people from Goguryeo, Baekje, and Silla, do not call them Samhan. How do you explain this when, by your logic, their identity was "Samhan?" The same goes for Japanese records.
I think you didn't answer this question, even though it was my fault you didn't see it. Do you have a counter-sample that is superior and contradicts the "small" sample?