Is it possible to copyright or trademark a company firm title?

By firm title I assume that you mean the name of the business - also known as the trade name. Trade names cannot be protected by copyright or trademark registrations. Trademarks protect the brand name of goods - Ford (brand) cars and trucks, etc. Copyright protects artistic products - books, movies, paintings, etc. Trade names can be protected under unfair competition laws - if another company seeks to confuse the public by having a name like yours - but this requires litigation to stop such activity. Hire a trademark lawyer to help you.

No, you can not copyright or trademark a company name. However, you may eventually be able to trademark the name if, in the opinion of the public, the word comes to mean the products or services of the company rather than just the name of the company.