Changing childs last name?

So we live in ca just got Temp full custody of my stepson hopefully it will be permanent soon. My bf is not on the bc and did not get to pick any part of the name his ex is an evil b*tch.... Anyway we picked name change forms & the clerk sd to ask mom if shed be willing to atleast add dads last name of course she said never. So we will be asking the judge for a court order and im wondering what are the odds that it will be granted? Is it possible? We have a son together who has dads last name and my poor stepson doesnt understand why hes not like papa and lil brother..... What can we do?