How can I legally change my sons last names?

Does anyone have experience with changing your child’s last name, legally. My boys are 14, 12, 8,6, same dad. He’s been in and out of their lives and I just won’t allow him to continue to mess wit my children’s emotions anymore. The older 2 already know what he’s like so they’re able to talk to me and I can see the damage he’s done to their emotions. Now my younger 2 are going through the same thing with him. He’s abandoned them too many times (as in disappears , goes MIA, then pops up when he wants to. He just had another baby a few months ago and it’s gotten so much worse. He does not help financially, I have full custody, he hasn’t seen them in months. He just makes promises he never fulfills and I always have to pick up his slack to comfort sad children. We were on and off for 15years, the last 6years together is when he started cheated on me again ( I was pregnant with my last son, I stayed, he became started being abusive again so I left, always supported my kids on my own. I divorced him 4 years ago and since then he’s been popping up whenever he wants to and I just will not allow it. His family is nonexistent in their lives. My younger boys are confused and have made comments asking why they have their dads last name “IF HE ISN’T EVEN HERE?” They always choose to use my family’s last name on their sports Jersey’s. My family has all boys, it’s just me my mom and my brothers. My father passed away 1 year ago and they were really close to him. I feel like it’s the right decision but wanted to know the process (I’m in CALIFORNIA) and also other peoples thoughts on that. He wasn’t very nice to them either way, that why we fought most of the time. He’s had DUI’s, 2 DV charges during our time together. Idk if that would help. My kids do go to counseling because they’ve expressed their sad feelings about him at school. It’s just too much to even list but he’s just no good. Should I even bother or just leave it alone? Thanks for reading.