How will it cost to rename your stepsons last name? My son is 15 and he wants my last name. We live in California

You will have to adopt him. In CA I believe the cost would be between $1500 and $3000, and if the bio father doesn't agree, almost impossible.

The total cost to change my son's name when he turns 18 years old? We live in CA

You have to call individual law firms and ask them - I'm assuming that's what you are asking about.

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Once he is 18 it's a different story. At 18 he can petition for a legal name change. He needs no one else's permission and unless there is an indication of fraud, it will be granted without comment. He can probably prepare the petition on his own and the only costs will be a nominal filing fee.