Is it better to register just a word or the name with the graphic?
The choice depends on the type of name you want to register. If the word you have in mind is as innovative as it is imaginative and completely new, it may be worthwhile registering only the name, thus preventing anybody else using that same name with any graphic.
If, on the other hand, the name is feeble, because vaguely descriptive of the product/service or because it reminds other similar words, then it is better registering both name and graphic, as it gains more value. For example, if we think about a famous trademark like “Coca-cola”, this has been considerate innovative and worth of protection in an absolute way just with the reference to the word “Coca” whilst the term of “cola”, a reminder of an ingredient of the beverage, has been regarded as weak and therefore freely usable, so other firms, i.e. Pepsi-Cola, have been able to use it quite lawfully. Such a trademark is protected even in its graphic part, as this has a strong nature not to be reproduced in any way by others.