Brand names and names that have been protected as intellectual property (e.g. registered trade marks) don't replace the need for a name of a food under the terms of the FIC. Neither do 'fancy names', names mainly used to market a food rather than give potential buyers absolute clarity about what it is.
A food name used in the EU member state of production and marketing can be used in other EU member states, with any necessary language translation. However, the FIC recognises that occasionally products can be named in the same way in different member states but are significantly different - if these are traded between member states, the name may need to be qualified by additional description so consumers aren't misled. Less often, a name used in one member state may be so inappropriate for the product in another member state that the same name cannot be used, even with qualifications.
The FIC gives no examples of names that may be subject to these additional restrictions. Businesses are responsible for identifying when such restrictions may apply to a name they are using.