If I’m in the process of buying a new construction home, can I add my kids’ names to make sure they are entitled to it if I die?

If you are already in a contract, you cannot modify that contract to add your children as buyer's without the other party's consent; even if you don't already have a contract, the other side would have the right to decline to enter into a contract if they don't want your children as parties to it (e.g. if any child has a debt issue or any relevant criminal offenses in his/her past, has filed bankruptcy, or otherwise has done something which would make the seller not want to contract with them; or is too young and so either still a minor or simply at an age that suggests lack of responsibility, income, or assets). Also, if you are applying for a mortgage or loan for this new home, you would need the lender's approval, too--they don't have to give out a loan if the don't like the proposed parties to it or the proposed ownership of the property.
Finally, you can't add a 13-year old to a home contract or real estate title.
There are ways to give your children a protectable interest in the home, such as by having a will which sets up a trust for their benefit if anything happens to you and which trust then gets the home, particularly if you also provide funding for the trust to pay any mortgage, taxes, etc. Do speak with a attorney about what you want to accomplish and how best to do it, but given the situation and the ages of the children, it's probably not by just adding them to the property at this point.