We have created separate budgets for each child under our sign-in information. If you look in the upper left corner under the budget screen where it says My Budget you'll see a drop down menu. One of the menu items is New Budget. You just click on that and it will take you to a new budget. We just renamed them with our kid's names. Hope that helps!
Ruth Elizabeth idea is definitely the official way. Another option that might be a good for you is to simply create a category group with the child's name as the title, and fill it with their categories.
Ideal if you only need a simple budget without the need for category groups (since you'll be limited to just categories) and your kids aren't actually doing any spending/budgeting on their own accounts that they want synced.
Otherwise, if you want the full-fledged experience, Ruth's suggestion is the way to go.