This is an interesting question of state law, but most states recognize a “right of publicity” at least to some extent.  The idea is that no one may use an individual’s name, likeness or other recognizable characteristics for commercial purposes without permission.  The definition of commercial use is not always clear and a nonprofit may argue that it is not a “commercial” operation.  Some states may apply the rule only to protect living people. But, assuming your father did not give his consent while he was alive to the use of his name on the building, you may have a reasonable case to prevent an unauthorized use, at least, perhaps, in the court of public opinion.  You should check with a local lawyer about your legal right to prevent the use.

You may want to take a different approach, however.  Naming rights can be very valuable.  You can usually find out how big a contribution is necessary to get naming rights on a charity’s building.  You can probably find out what a business has paid to put its name on a stadium or a transit center in your area.  You could offer to sell the naming right to the organization for a similar amount if they really want to use your father’s name on their building.  With no disrespect meant for your father, they might find that there is someone else they would like to honor.

For more information on naming rights consider this text;

Naming Rights: Legacy Gifts and Corporate Money
By Terry Burton
In 2007 the sale of naming rights brought an estimated $4 billion in revenue to the nonprofit sector What slice of the pie did your organization enjoy? From transformational gifts to naming traditions to pricing strategies for capital campaigns, Naming Rights offers you a vivid collection of contemporary information that your organization can use today. Can your development team quickly pull together an accurate benchmark report? Learn how to benchmark and compete with peer organizations for buildings, spaces, and named endowments. Setting the ask amounts for your naming opportunities is critical to closing the deal. Are you ready?