If you're that hostile toward your husband, you definitely should not keep his name. It'll make you fume. But unless there is some extreme issue that means their Dad won't be in their lives anymore, it would be absolutely rotten of you to change your kids' names (and equally rotten to raise them with the pressure of having this future choice hanging over their heads: When I'm 16, I have to choose between my parents. I have to pick between disappointing my Mom by keeping my Dad's name, or making my Dad feel rejected by taking Mom's name).
If you and your STBX originally decided the kids should have your maiden name, as some open-minded, modern nod to the value of mothers and/or a rejection of ancient, sexist traditions, that's perfectly fine. But if, prior to the divorce, you saw fit to follow the tradition of taking your husband's name and giving his name to your children, do not change it now. I'm sure you're angry with him. Maybe you have good reason to be. But please think about it from their perspective, not your own. It's their name.
The choice to give them his name when they were born was a symbol of the importance of his role as their father. Once you chose to make that symbolic gesture, the choice to take away that name necessarily symbolizes a lessening or termination of the importance of his role as their father.
Certainly, YOU may feel that if you get sole custody, he will become the less important parent and you will become the more important one. But YOUR CHILDREN are not divorcing their father. THEY are not choosing to change their relationship OR their living arrangements with him. And there are all sorts of reasons a parent is given sole custody, which do not mean that the other parent has ceased to be important, or ceased to be a parent. Sole custody is standard when parents stop living in the same town, it's also common in high conflict cases, where the court cannot expect the parents to be able to resolve ANYthing jointly. It is often a practical matter, NOT a statement by the court that one parent has ceased to be a parent.
If you get sole custody, the simple fact that the children will spend more time with you and you will be entitled to make all the decisions about their lives without consulting your ex will clearly demonstrate - to you, the kids and everyone you know - that you have the bigger parental role. If you ALSO make a show of changing their names to yours (IMO) that would be the adult equivalent of sticking your thumbs in your ears, waving your fingers around, sticking out your tongue and yelling, "Nah-nah-nah, boo-boo!"
Changing children's names during/after a divorce - changing their last names or even mandating that they stop using a nickname the other parent calls them - is one of the common actions of a parental alienator. Try to resist the impulse. The divorce will be hard enough for your kids, without you doing passive-aggressive things to sabotage their already-more-difficult relationship with their father.
If your husband spends the next however-many years until your kids are adults being such a lousy father that your kids INDEPENDENTLY come to you and say, "I want to take your name," then that will be a wonderful, well-deserved moment of vindication for you, I'm sure. I wouldn't begrudge you some happy tears, over that. But you should not ever bring up to them that they HAVE a choice to make. NO MATTER HOW YOU PHRASE IT, they will know that you have it in your mind that they MIGHT take your name. From that moment forward, they will feel that they're choosing between their parents. Each year that they continue using their father's name, they will feel some guilt that you might be secretly disappointed or feel secretly slighted. And if they DO take your name, how could you be sure they WANTED to, and that they don't just feel more obligated to please you, than to please your ex? If you're going to let it be "their choice", REALLY let it be that, by never bringing it up.