Yes. "Son" is his last name.
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nothing is diffrent son is gukus last name that's why they call him son goku.
Skips is goku ssj 8, who travel back in time.
Goku doesn't have a third son. He only has Gohan his first son and Goten his second son.
He doesn't have one, but his full name is Son Goku.
Gohan and Goten