No, it does not.
Trademark protection applies whenever the customer is likely to confuse a name/picture/etc. for a registered trademark. In some jurisdictions, it even goes as far that protection applies whenever it is likely that the marking is associated with the registered trademark.
As Singulaere Entitaet points out, trademark law does not prohibit every single use of a name. For instance, most trademarks are specific to a certain class of products. However, that does not mean that every use outside of this class of products is permitted. The exact details are too complex for a single answer and beyond the scope of htis question.
Source for last sentence of first paragraph: I don't have an online source, but that's the way I learned it in my business administration class.