There is a lot more information needed to begin to answer your question. It doesn't matter if your father was "in charge" of the business in Denham Springs. What matters is who owned the business and how was the business set up? It is possible that your father ran the business, but someone else owned the stock in the business or that there was some sort of contract or agreement regarding teh transfer of the business in the event of his death.
It also matters very much whether your father had a will. If he had a will then you are only entitled to what the will provides for you and it is possible that the will transferred the business to someone else.
Finally, it matters whether the business owed money to anyone and whether any such debts were secured by the business or its assets. You cannot inherit property that is already pledged to a creditor unless you are prepared to pay off the debt.
Being named after your father gives you no extra legal rights. You and your two siblings are the default heirs and are entitled to inherit what your father owned when he died, but he was entitled to make other arrangements and not give you anything if he wanted to.
You need to find out how the business was owned, whether your father had a will, and whether the will was probated. You will want to contact a probate lawyer in Louisiana if it is important to you to pursue these matters.
You can reach Harkess & Salter LLC at (303) 531-5380 or info@Harkess-Salter.com. Stephen Harkess is an attorney licensed in the state and federal courts of Colorado. This answer is for general information only and does not create an attorney client relationship between Stephen Harkess or Harkess & Salter LLC and any person. You should schedule a consultation with an attorney to discuss the specifics of your legal issues.
The answer above is right on point. If you want to pursue this, you will eventually need to work with an attorney to review the ownership structure of the business and your father's will or the governing State's default distribution provisions. Good luck!
As you know, I am not your lawyer and by providing this answer, we have not entered into an attorney/client relationship. This answer is provided on Avvo for general informational purposes only. If you desire legal advice, please consult a lawyer licensed in your jurisdiction and form an attorney/client relationship.