Legal Question in Wills and Trusts in Missouri

If the business was incorproated, then the business can change its name like any other corporation would. If the business was just the father-in-law's name, then his heirs might still beable to operate the business under that name or change it, so long as they do not mislead partners or customers of the death of father in law. The question is really "who owns the assets and owes the bills of the company?" and that determination requires many more facts than you can provide here. You might consider consulting directly with an attorney in your area. Many offer a free or low cost initial consultation.

Good luck