If there has been no previous probate or administration proceeding, and the estate is under $30,000.00, you can start a small estate administration in Surrogate's Court in the County of your father's last residence. This is a simplified procedure that you may be able to handle on your own. Forms and more information can be found here: http://www.nycourthelp.gov/diy/smallestate.html
If your father had a trust you could open up an account in the name of the trust or establish an administrative trust. You can apply for a tax ID number for either of these trusts. Then open an account in the name of the trust and deposit the check into the account. You can name the administrative trust "The Estate of ___________ Administrative Trust".
Any individual seeking legal advice for their own situation should retain their own legal counsel as this response provides information that is general in nature and not specific to any person's unique situation. Circular 230 Disclaimer - Advice given in this response cannot be used to eliminate penalties with the IRS or any other governmental agency.
I see two options here: First, if your father created a lifetime trust of which you now are serving as successor trustee, you could ask the person who sent you the check to issue you a new check in the name of your father's trust. That would eliminate the need for a court proceeding and the opening of an Estate account. Second, if you have not already been appointed estate representative by a court, you can apply to the Surrogate's Court in the county of your father's last residence to be appointed representative of his Estate. If the aggregate value of the assets in your father's name (including the check you reference) is $30,000 or less, you can commence a small estates proceeding; this is a fairly simple process and the Surrogate's Court clerk will have forms for you, or you can download the forms online. If the aggregate value of the assets in your father's name exceed $30,000 in value, you will need to probate your father's will, if he has one, or commence an intestate administration proceeding with the Surrogate's Court.