First, I assume by a "general name" I assume you mean a name that is generic description of the type of goods, such as clothes for clothing. Such terms are not registerable/protectable. However, if you have a unique logo, it would be protectible/registerable with or without the descriptive term. Furthermore, if you file for the combination of the descriptive term and the logo, you will be required to disclaim the descriptive term apart from the combined mark since you cannot preclude others from using terms that are comonly used to describe or identify a particular product.
Answered on Apr 01st, 2014 at 3:57 PM